Why were the apostles still going to the temple for prayer and rituals?

All the Torah is valid today. Paul and the Apostles lived the Torah as Yeshua (Jesus) taught them to do so. Sacrifices continued by believing Christians until the temple was destroyed. Paul had to make sin sacrifices according to Numbers Chapter 6 to complete the Nazirite vow for those men in the verse. Sacrifices were never given to take away sin. Sacrifices were to humble us, come near, and be reconciled unto God. It is a form of worship and one that will be restored when Yeshua (Jesus) comes to establish His physical Kingdom on earth. He will rule and reign and we will go and bring our offerings to the temple once again.

For example the festival of Sukkot / Tabernacles requires a multitude of sacrifices to take place—the nations will gather there (future context):

Then the survivors from all the nations that have attacked Jerusalem will go up year after year to worship the King, the LORD Almighty, and to celebrate the Festival of Tabernacles. (Zechariah 14:16)

First of all, let me say that I liked L1R's answer and upvoted it. Let me add to the discussion.

(1) Old habits die hard. Anyone who is a member of a regularly proselyting church knows that converts require time --- often years --- to fully adopt the habits, behaviors, and culture of their new faith. The Apostles were no different. Consider Acts 11:4-10, which says in part...

Upon the which when I had fastened mine eyes, I considered, and saw fourfooted beasts of the earth, and wild beasts, and creeping things, and fowls of the air. And I heard a voice saying unto me, Arise, Peter; slay and eat. But I said, Not so, Lord: for nothing common or unclean hath at any time entered into my mouth.

This is Peter after he had spent years with the Lord and after he had witnessed the resurrection --- and yet he was still following a habit that he had been taught in his childhood and had obeyed nearly his entire life.

The issue of circumcision was also a hot topic.

Acts 10:45--- And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.

It took time, probably a lot of time, for the followers of Christ to fully understand and accept the idea that they were no longer bound to the Judaic law.

(2) The temple of Christ's day wasn't simply a place were sacrifice was performed, it was a place of teaching and preaching. In John 10:22-31 we find Jesus teaching in Solomon's Porch, which was inside the Temple. What He said there constituted both blasphemy and heresy to practicing Jews, so they took up stones to kill Him. Your reference to Acts 3:1 is a good example of this. Had you read the entire story (Acts 3:1-11), you would have noted this.

(3) Finally, there is the very practical concept that L1R brought out... people were getting stoned for being a Christian. Remember Saul/Paul. In Acts 8:1,3 we find...

And Saul was consenting unto his [Stephen's] death. And at that time there was a great persecution against the church which was at Jerusalem.... As for Saul, he made havoc of the church, entering into every house, and haling men and women committed them to prison.

It's no wonder at all that Christian leaders at the time were telling Christians ... and especially Jewish converts ... to go about living the Law of Moses. It kept them alive.

There are a few things to consider. First of all, the Jewish Ceremonial and Civil Laws have no bearing on US today. For example, i live in the U.S. and am a gentile christian.

Therefore the laws of Israel, and the regulations of Judaism have no bindings on me.

These people were still living in Israel, and were commanded by Jesus to follow the laws of the land

Matthew 22:20-21

And Jesus said to them, “Whose likeness and inscription is this?” They said, “Caesar's.” Then he said to them, “Therefore render to Caesar the things that are Caesar's, and to God the things that are God's.”

This is specifically about Taxes, but the Epistles of the new testament expanded on this idea of obeying the law.

1 peter 2:13-14

Therefore submit yourselves to every ordinance of man for the Lord’s sake, whether to the king as supreme, 14 or to governors, as to those who are sent by him for the punishment of evildoers and for the praise of those who do good.

So, they would have been required to follow the Laws of their Jewish state.

Also, in the book of Acts we see the Peter, and also Paul would often go to the Synagogues to Preach, offering the Gospel to the Jews First, and then the Gentiles.

rom 1:16

16 For I am not ashamed of the gospel of Christ,[a] for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek.

In this Evangelistic context, it was important that Paul and his companions would not give the Jews any extra reason to stumble!

1 Corinthians 9:19-21

19 For though I am free from all men, I have made myself a servant to all, that I might win the more; 20 and to the Jews I became as a Jew, that I might win Jews; to those who are under the law, as under the law,[c] that I might win those who are under the law; 21 to those who are without law, as without law (not being without law toward God,[d] but under law toward Christ[e]), that I might win those who are without law

Jesus had to send a special vision to Peter, showing him that no longer the gentiles and their foods were unclean in his sight. Acts 10:11-16

11 and saw heaven opened and an object like a great sheet bound at the four corners, descending to him and let down to the earth. 12 In it were all kinds of four-footed animals of the earth, wild beasts, creeping things, and birds of the air. 13 And a voice came to him, “Rise, Peter; kill and eat.” 14 But Peter said, “Not so, Lord! For I have never eaten anything common or unclean.” 15 And a voice spoke to him again the second time, “What God has cleansed you must not call common.” 16 This was done three times. And the object was taken up into heaven again.

So the situation was a bit different for Jewish Christians, living in Israel, Than it was for Gentile Christians, especially outside of the country of Israel.

In your question you say

How is it that they didn't understand modern day Christianity that the law was abolished and that sacrifices where of no use since Jesus cleared that for them?

I think that saying the law was abolished is taking it to far.

Jesus himself said

For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled.

--Addendum to address the comments.

I am in no way trying to promote legalism (attempting to obey the law to gain God'ds favor/Salvation). I am just saying, that there is nothing wrong with following the law. It is Paul who told us in Romans 7:12

12 Therefore the law is holy, and the commandment holy and just and good.

The unique message that the Apostles taught, was that the Law could in no way Save us. The Law only shows us our sins! Romans 3:20

20 Therefore by the deeds of the law no flesh will be justified in His sight, for by the law is the knowledge of sin.

So, the Apostles were not in any way "against" the law. They just realized that Christ could save us, something the law never had the power to do.

Where Paul specifically got very upset, was when Jewish people tried to force obedience to the outward jewish traditions/laws onto believing Gentiles. Or when people tried to teach that following the law was required for salvation.