What is the difference between изполвам and ползвам ?Feel free to just provide example sentences.

I think Ive answered this one, theyre the same really. Ползвам is more informal.

But there is a use case which is a bit specific...

използвам implies using all of something until it ends, while ползвам would be used more rarely for that

използвам целия крем
use the whole cream

the prefix из sometimes implies doing something thoroughly and fully, carefully

мия wash
измивам wash but also more thoroughly in a sense

чистя clean
изчиствам clean but also more thoroughly or carefully in a sense

вземам take
изземам take away everything or by force

кажя to say
изкажя to express yourself, give something like an opinion or finish a story until the end

пиша write
изпиша write out in full, also write with a pen until it is empty and no ink is left