I must learn English 和 I have to learn English 和 I've got to learn English 和 does the first stance express/stress my own desire to study English unlike the rest? 的差別在哪裡？如果不好說明，請提供一些例句。

Yes, you're correct. There are very minor differences between the phrase, and most people will understand them to mean almost the same thing.

"Must" is a little more formal and you're correct - it expresses that the desire comes from yourself vs. an external force (i.e. a rule or person making you do something).

"Have to" is less formal (but not informal) and could mean that something external is pushing you to do something.

"I've got to" is the same as I have (got) to - same as above, though sometimes people drop "have" and say "I got to..." which is technically slang, making it informal but it's very common and I wouldn't cause much confusion.