According to Catholicism and/or Eastern Othodox, if we have Guardian Angels do we also have an assigned Demons?

Although the expression “guardian angels” nowhere appears in the Bible that does not mean the concept is without foundation. The Bible has much to say about angels, and there are plenty examples of how angels have ministered to individuals. Here are just a few verses that indicate the power of angels who protect God’s people:

The angel of the LORD encamps around those who fear him, and he delivers them” (Psalm 34:7).

If you make the Most High your dwelling – even the LORD, who is my refuge – then no harm will befall you, no disaster will come near your tent. For he will command his angels concerning you to guard you in all your ways; they will lift you up in their hands, so that you will not strike your foot against a stone. You will tread upon the lion and the cobra; you will trample the great lion and the serpent” (Psalm 91:9-13).

Jesus also spoke about angels that appear to be assigned to children:

Matthew 18 10 See that you do not despise one of these little ones; for I tell you that in heaven their angels always behold the face of my Father who is in heaven.

As for demons, Origen and Athanasius had quite a lot to say about them and their influence. Here are a few brief extracts from Catholic scholar Boniface Ramsey:

Chapter IV, The Human Condition – re. “the influence attributed to demons in human life. This too was a result of the fall. So great was the demonic influence felt to be that Origen devotes a chapter of his work ‘On First Principles’ to “how the devil and the opposing powers are, according to the Scriptures, at war with the human race.”

Ramsey points out that Origen “expends much of his effort, however, on putting the demons’ role into perspective. Some simple Christians think, Origen says, that the demons’ powers are so overwhelming that they drive people into sin, and that if there were no demons there would be no sin. But this is not the case; sin arises from within, and the demons take advantage of our sinfulness and aggravate it, although they do in fact introduce some evil thoughts into our hearts as well. In any event, we are not alone in the fight against the evil powers, since there are good spirits too who come to our aid. Here Origen recalls a passage from the second-century Shepherd of Hermas, which speaks of two angels in the human person, one of righteousness and one of wickedness, each competing for his soul.

It is in monastic and more especially in desert literature that we find the consciousness of the demonic influence raised to its highest pitch. Athanasius’ Life of Anthony is virtually a treatise on demonology, and in it we are struck constantly by the conviction that the demons are ubiquitous and inescapable: “There is a great multitude in the air around us, and they are not far from us.” For chapter on chapter Anthony speaks of their powers of transformation, deception, vision, and their ability to confuse and terrify the souls of the unwary.

The fact that the most important theologians, men of the calibre of Origen and Athanasius and Augustine, spend pages on the demons indicates that belief in their power was not restricted to the superstitious or to unschooled monks; it was simply a datum of early Christianity that was accepted by all.” Source: Boniface Ramsey, O.P., ‘Beginning to Read The Fathers’ p65-66 (Darton, Longman and Todd, London, 1985)

The Catholic Catechism has this to say about angels who guard, protect and shepherd:

335 In her liturgy, the Church joins with the angels to adore the thrice-holy God. She invokes their assistance (in the funeral liturgy's In Paradisum deducant te angeli... ["May the angels lead you into Paradise. . ."]). Moreover, in the "Cherubic Hymn" of the Byzantine Liturgy, she celebrates the memory of certain angels more particularly (St. Michael, St. Gabriel, St. Raphael, and the guardian angels).

336 From its beginning until death, human life is surrounded by their watchful care and intercession. 202 "Beside each believer stands an angel as protector and shepherd leading him to life." 203 Already here on earth the Christian life shares by faith in the blessed company of angels and men united in God. Source: http://www.vatican.va/archive/ccc_css/archive/catechism/p1s2c1p5.htm

Judaism also believes in ministering angels, both good and evil:

The Talmud records a teaching that two ministering angels — one good and one evil — accompany a person home from synagogue on Shabbat evening. If they find the person’s home prepared for Shabbat, the good angel declares: “May it be Your will that it shall be like this for another Shabbat.” And the evil angel answers against his will: “Amen.” If the home is not prepared, the reverse happens: The evil angel voices a wish for it to be this way for another week and the good angel responds “Amen.” Shalom Aleichem, a liturgical song welcoming angels into the home before the Sabbath meal, is inspired by this teaching.

Angels are singular and unchanging in their essences, Steinsaltz writes, and can be either good or evil (demons), the latter the product of human beings doing the opposite of a mitzvah — harboring evil thoughts or committing acts of wickedness. Like good angels, evil angels also act in a dual fashion — bringing evil from the spiritual to the material world by inspiring sin or causing suffering and punishment, while also receiving energy from the misdeeds of human beings. “To be sure, were the world to root out all evil completely, then as a matter of course the subversive angels would disappear, since they exist as permanent parasites living on man,” Steinsaltz writes. “But as long as man chooses evil, he supports and nurtures whole worlds and mansions of evil, all of them drawing upon the same human sickness of soul.” Source: https://www.myjewishlearning.com/article/angels/

There is no doubt that angels and demons exist, but nowhere in the Bible does it say a specific angel is assigned to guard individuals. Nor is there any suggestion that God appoints a demon to vie for the soul of a person. Indeed, why would God do such a thing after a person has come to saving faith in Christ Jesus? Key to this question is the understanding that all who have been redeemed, all who belong to Christ Jesus, are protected from evil. Does not Jesus promise all who belong to Him that they will be recipients of the Holy Spirit? “What fellowship can light have with darkness?” (2 Corinthians 6:14)

A “guardian demon” is a contradiction in terms. Demons have no interest in ministering to the elect, to those who have been redeemed by the blood of Christ. Their sole purpose is to prevent people from being saved. God’s purpose is to draw people so they can be saved. Why, even from before the creation of the world “he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will... Having believed, you were marked in him with a seal, the promised Holy Spirit, who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession- to the praise of His glory” (Ephesians 1:4-14).

Jesus says of the little ones who make up the kingdom of heaven :

Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven. Matthew 18:10 KJV.

So, yes, I also believe that the children of the Father, born from above, redeemed by Christ, have angels (one at least) "assigned" to them.

From the incident regarding Peter, quoted in the question, it seems clear to me that the angel which assisted Peter to escape from prison had probably helped him previously and this was known among the church, therefore they said (on this occasion), 'It is his angel' because they were already acquainted with the angel's existence and guardianship.

The redeemed, previously, were indwelt by unclean spirits, demons, as we see in many places in the gospel accounts. Out of one man, the Gadarene, there went a whole legion of demons, enough to cause a whole herd of swine to rush off a precipice into the sea, Matthew 8, Mark 5, Luke 8.

Out of Mary of Magdalene, there went seven demons, and she was delivered of them.

And certain women, which had been healed of evil spirits and infirmities, Mary called Magdalene, out of whom went seven devils, Luke 8:2 KJV.

Jesus warns us that, being once delivered, and the house (of our soul) being 'swept and garnished' we should not have the place just . . . vacant.

When the unclean spirit is gone out of a man, he walketh through dry places, seeking rest, and findeth none. Then he saith, I will return into my house from whence I came out; and when he is come, he findeth it empty, swept, and garnished. Then goeth he, and taketh with himself seven other spirits more wicked than himself, and they enter in and dwell there: and the last state of that man is worse than the first. Matthew 12:44 KJV, also Luke 11:25.

Those who believe the gospel and follow Jesus Christ are to be full of the Holy Spirit and are advised, by the apostle Paul :

That ye put off concerning the former conversation the old man, which is corrupt according to the deceitful lusts; And be renewed in the spirit of your mind; And that ye put on the new man, which after God is created in righteousness and true holiness. Ephesians 4:22 - 24 KJV.