Man United will stick with him til the end of the season imho.
No. People are just speculating just for the fun of it. If they do lose to Burnley however it's not going to look good for him. I don't think they will stick with him until the end of the season unless he turns them around pretty quickly. They should beat Burnley but they are usually very strong at home and tough to beat. Zidane would be a worthy successor and I'd like to see him at United if Jose does go, but they're just rumors and mostly speculation and wishful thinking from excited fans. As I said before as well, even if he did manage them I don't think he'll be a miracle worker and do that much better than Jose would have done.
It will be a miracle if Zidane replace Mourinho, if there is other coach that is able to replace Mourinho then that would be zidane. Look at how he changed Real Madrid, he won 3 times champions league trophy and currently not coaching any team. If Manchester United keep playing like this then Mourinho might really lose his job