does anyone actually know the process for america claim a new territory or adding a new state??

It is called taking over. Invading. Brutality. Expansion. Colonization.
It's illegal.
The process is evil.
Hope you're not still on the fence, but I've met the West. You're wondering.

Depends on the leader, and the era and the circumstances. It hasn't been consistent.

You have some states that were of the original colonies, some that were bought outright and places like Hawaii that was straight up annexed by Trump's idol McKinley ironically enough.

It's not part of the second amendment?

Try ArtIV.S3.C1.1 Overview of Admissions (New States) Clause, but I know you're being modest because all MAGAs memorize the Constitution.

statehood requires an act of congress with a majority vote from house and senate

territory/annexation requires president initiate a treaty with 2/3's senate vote

as for stars on flag, the easiest solution would just be to throw Minnesota out of Union and have Greenland or Alberta take it's spot... 😏