By default key on new sheet stuck in A major

It's not clear what you mean, but if you can attach your score and post precise steps to reproduce the problem, we can understand and assist better.

Note that the key of B minor is concert D minor, so if that's the key you'd need to specify if you want it to show as B minor on your alto sax part. You always need to specify keys in concert pitch so that MuseScore can transpose it correctly for all the different instruments in your score.

The alto sax is a transposing instrument in E♭. That means that every note you play sounds a major sixth lower.

Examples:
• If you play a C4 you can hear a E♭3.
• If you play an A major scale from A4 to A5 you can hear a C major scale from C4 to C5.

In MuseScore you input the sounding key signatures. The sound of B minor (2 ♯) is played as G♯ minor (5 ♯, that’s probably what you mean when you say “B minor AND A major”). If you want to play B minor it will sound as D minor, so you have to input D minor (1 ♭).

At the bottom right of the window there is a checkbox labelled “concert pitch” meaning “show what is heard instead of what is played”:

Try to write some notes and toggle this to see the difference.