What are the main differences between the Catholic Popes and the Mormon Prophets?

The main difference between the Prophet and the Pope is that the Prophet has authority to lead and direct the church, whereas the Pope does not.

To be more specific: The Prophet has the proper priesthood authority, as was given to Peter.

18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.

19 And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven. Matt 16:18-19

In that act, Christ gave Peter authority to lead and direct the church. It was then established that the head of the church would be chosen from one of the twelve apostles. A pattern of determining whom should fill vacancies in the Twelve was also established:

22 Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection.

23 And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias.

24 And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen,

25 That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place.

26 And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles. Acts 1:21-26

In the years that followed, all the apostles were martyred. The vacancies in the Twelve were not filled, the line of apostolic succession was broken, and those keys were lost.

It was not until the time of Joseph Smith that those priesthood keys were restored to the earth, when Peter, James, and John appeared in the flesh to Joseph Smith and Oliver Cowdery, and conferred upon them the Holy Priesthood of God.

Without the priesthood, and the keys of revelation, the Pope cannot commune with the Father, and has no authority to speak on his behalf.

Note: My knowledge on Catholic beliefs is spotty. If anyone Catholic wants to go ahead and fill in the gaps, go ahead. I do not intend to offend any Catholics with it.

When you prophets, I will assume you are talking about the President of the Church, not the other non-president prophets (i.e. members of the Quorum of the Twelve Apostles).

Before I go on to your six questions, I would like to note the main theological difference: The Pope claims to be able to receive no revelation, but rather is making decisions based on what he thinks is best, and according to scripture. The prophet claims to use both scripture and revelation from God (hence the name) instead of his own decision making.

Anyways, to your six questions.

(1) If both claim the Petrine Seat(by succession or?).

They both claim to succeed Peter in being the head of the true church of christ, in a documented line of succession from Peter to themselves.

(2) If both have a College of Bishops/"Highest Teachers" in union with the Pope or Prophet.

I do not know about the Pope, but in the LDS Church there are (usually) 14 other prophets in addition to the prophet. These prophets are also Apostles, seers, and revelators.

(3) If both have universal jurisdiction as universal pastors of their respective churches. Meaning that they can operate in all churches as if they were the head of those individual churches, no need to appeal to the locals.

I assume the Pope may do so. The Prophet has all the keys of this dispensation, including the leading of local congregations. He usually does not "usurp" local congregations though, since his main duty is being a prophet.

(4) If both are completely immune from stepping down from the office unless it is their own decision to step down.

I do not know about the Pope. The prophet is subject to God, who can remove him from office if he attempts to lead the church astray (see Official Declaration 1). Additionally, he is subject to disciplinary council of the church if he commits a serious sin.

(5) If believers are encouraged to listen to the leader above any other in the hierarchy in case of disagreement between the leader and others on none dogmatic issues, as well as disagreements outside of the Church on politics for example.

I assume this is true of the Pope. It is generally recognized in the LDS Church that the Prophet is more accurate than local leaders, though both try to stay in harmony with God (and therefore with each other, indirectly).

(6) If both claim to be infallible under certain conditions(if so what are they?) by virtue of their office in the eyes of God.

I'm not sure about the Pope. For the LDS Church, see What does the LDS Church teach about infallibility?.