Can you have a live in mate while having visitations every other weekend with child?

I'm from Canada and my exhusband had a live in partner and her kids living with him while our children visited him on alternate weekends.

Yes unless it is written in an official document like your divorce.
Yes but if the other parent finds complaints such as abuse and drug usage they can have CPS investigate and it can be a possible problem then.

Yes.

Unless your coirt ordered visitation prohibits it, you can. However, it could spur the other parent to have the agreement modified to include it.

Yes, there may be a few specific court orders that prohibit it with specific partners and other issues, but unless it has specificly been ordered against, it is OK