In a 4/4 time signature, can I write a half note on the 2nd and 3rd beat Or should I split the half note into quarter notes with a tie to show the middle of the bar?
Also, in 7/8 with (4,3)as main beats, can I write 8 beamed 16th notes and the the rest of the beat?
In relatively strict notational convention, you'd want to split that half note into two quarter notes. But honestly, I've seen that particular rhythm countless times; it won't trip up any performer. (What could trip up a performer, though, is cutting over smaller divisions of the bar like a quarter note or eighth note.)
And your 7/8 sounds fine, but you may also experiment with two groups of four beamed sixteenth notes. This is only because we're used to seeing groups of four and can recognize them pretty much immediately. A group of eight, though, is less common, and it may cause a performer to second guess themselves.
