could [a minte to spre] mean that a minute concerning the man who spares a minute for another man or work?-- No; there is no reference to another man. Try again.
In [I'll have time to see you on Monday.], could [time to see you on Monday] mean that
1. You say "Better!" to me, I am uncertain as to it. If means [You would do better to get my advice.] or [You would be better to get my advice.]?-- No! It means [you did better!]
2. And why not [a minute to be spred]?-- 'A minute to spare' is a fixed phrase.