I did not want to pull a trigger off of another rifle. Will a factory 700 trigger and safety fit a Rem 722?

Yes, no problem.

Yes, but a small problem. Yhe safety lever on the 700 trigger will not clear the side of the receiver on the 722. You will have to replace the safety lever with the 722 lever or, have someonw mill out the side of the receiver on the 722.

To add to what eddie said,the 722 safety lever "dentent" hole won't match up with a 700 trigger housing,and a 700 trigger lever will set much further back in the 722 trigger guard,to the point of not allowing you to pull the trigger.You can carefullly bend a bigger bow in the 722 trigger guard or carefully bend the trigger lever foward to clear.Most 722/721 triggers are pretty good,and will safely adjust to 2# maybe a bit less with some polishing on the sears.