1. What if a man or woman marries with the intention to divorce later while the other marries with the intention of permanent marriage?
A: The marriage contract would be valid, i.e. not zina, but he would be guilty in the sight of Allah of ghish, which is akin to lying and cheating, because the spouse is under the impression of permanence.
2. What if both the man and woman marry legitimately through nikah shar'i with all the requirements, but they marry with the intention of getting divorced after a certain amount of time, will the marriage still be valid or would it become mut'a?
A: If it's an intention in their hearts within themselves, then it's as above. However, if at any point they spoke about it to one another, even if they did not write it in the contract, then it is still considered mut'a, because marriage is not just by the written word. Oral agreements and committments count and are no different from written ones.
3. What is a misyar marriage and is it similar to mut'a?
A: Misyar marriages, i.e. the traveler's marriage or more literally, the on-the-go marriage, are when both sides agree to wave and forgo certain rights. For example, the woman would forgo her right of financial maintenance. They would both forgo co-living. Etc. However, there is no time limit or expiration date on a misyar marriage, and for that reason it is not mut'a.
The scholars view misyar marriages with some circumspect, because it does not fulfill the basic elements which are the point of marriage, such as living together, the husband supporting the wife and having a family. Others have recognized its value in certain circumstances, for example women who are older, independent and may be busied with a career, but would like a long-distance relationship. Further, there is no text in the Shari'a forbidding a woman to forgo certain rights. In sum, while many scholars dislike the misyar marriage, they cannot say it is zina. Mut'a in contrast is zina if the one doing it has been informed that the Prophet peace be upon him prohibitted it and that the umma has ijma' on the soundness, meaning and finality of those hadiths.