Hello, Language learner, and welcome to the Grammar Exchange.
1) I work as a programmer, mostly building ASP.NET applications with SQL Server as the database.
Question 1): Can we remove the comma, without changing the meaning of the sentence?
Question 2): Is sentence 1) equivalent in meaning to:
I work as a programmer. I mostly build ASP.NET applications with SQL Server as the database.
Those are interesting questions. I'll give you my opinion and hope David, our moderator, can give us his view.
I think that "mostly building..." can be parsed as a relative or an adverbial clause:
1.a. I work as a programmer who mostly builds ASP.NET applications with SQL Server as the/a database.
1.b. I work as a programmer mostly by building ASP.NET applications with SQL Server as the/a database.
According to your question (2), the meaning you want to convey seems to be closer to 1.b., because the subject of "build" is "I" rather than "all/some programmers" even though, being a programmer, you claim to be one who builds that kind of applications.
In answer to your question (1), I think the comma can be omitted but should perhaps be kept because it would otherwise sound like a restrictive relative (1.a.).