Nós temos muito a fazer ?? Is it correct ?
Yes, it is also right.
Might I put "Nós temos bastantes coisas para fazer"?
Yes, less common, but also right. "bastante coisa" is more common.
Why is "o que" correct here? To me it looks like "We have a lot what to do."
why is 'o que' here instead of either 'para' or 'a'?
"nós temos muito por fazer"..... will that work??
Yes, not so usual though.
What do "o que" here mean?
Why is "temos muitas coisas que fazer" wrong, I naturally thought of that.
'Nós temos muito a realisar' is not accepted?
"...a realizar" should be accepted also.