I hear Poles say "Będę jutro (czasownik) coś..." Why is placing the time before the verb wrong?
It's okay, it's accepted, but because of some mistake the male forms (myślał) were missing from the potential answers, added them.
I happened to write the subjective pronoun and it didn't work. Is it actually wrong to say "ja będę..."?
That's an oversight. Using "ja" can very often be a bit clumsy, but it's definitely not wrong. Added now.
Pomysle o tym jutro. Moze byc?
I think that's rather a translation of "I will think about it tomorrow" and not of "I will be thinking" which puts emphasis on the process.