Ah yes GENITALIA!
I don't know all the details, especially when it comes to Phalloplasty. Vaginoplasty does not actually involve chopping stuff off and throwing it away but sorta inverting the penis into a vagina and vulva. After all there's so much sensitive nerves and stuff in the penis that can be used for sexytimes and it would be a shame to toss it!
Wkipedia goes into all the nitty gritty details here
and here (with pictures )
Hormones also generally have an effect, if one is one estrogen and anti androgens then the penis will stop being able to produce viable sperm, spontaneous erections often go away, and the penis will get all cute and tiny! I hear testosterone makes the clitoris bigger and more penis-like, but again less familiar with all that.
As far as dysphoria, there's a wide range of ways people experience gender dysphoria. Some people might not get it as strong as others, or be triggered by different things. I hate shaving and it can send me into tears, so will often walk around with beard stubble, whereas other people might not be able to stand beard stubble at all but be fine shaving. And some trans people might not have dysphoria at all.
So some trans people might not even want any given surgery, or be able to justify the cost, or want surgery but not be able to afford it. Similarly some trans people don't go on HRT for various reasons. So yeah, no way to tell any particular trans persons thoughts or desires regarding hormones or various surgeries or dysphoria unless they tell you (and lots of this stuff is generally considered pretty private, so I wouldn't go around asking)
One last thing, some people like "MtF" and "FtM" as descriptors so I won't say to not use it entirely, but I will ask to please avoid using it as a noun. I'm not an MtF the same way I'm not a crazy, etc.
I also prefer "trans person" / "trans man" / "trans women" to "MtF women", because it feels more general and inclusive to me and less shoehorning people into narrow roles.
And "trans person/man/woman/etc" doesn't depend on a gender binary.
And it doesn't imply trans people are going from one gender to another.
Thanks for the question, hopefully I didn't come across too intimidating ^_^!