LVL Calculater help

This is a bearing wall 13' wide with a 48'' opening in the middle 1-2x10 header Im wondering if this are problems and how to fix them before hanging the drywall King stud other side not nailed to top plate. Should I nail it same as the other side? Trimmer not nail to header Is this OK? Not visible but header is not bearing on trimmer other side[1/8 gap] Should I shimmy it? Othar studs/ top plate no visible nails Is this OK? Top plate bears only on half of stud Should I sister with a full lenght stud to existing and also nail it to the top plate ? Can I substitute nails with screws? Thanks a lot

:wall:We are remodeling the bathroom and it requires that we move the heating register. We have a forced air system.To do that requires that one floor joist be cut....How can we reinforce the joist...? This is on the second floor.