so I need to mount my RD hanger on my new frame, so do I need to use something like blue lock tight on the screw as a safety measurer?

You can if you want. Don't overdo it. And the term is loctite.

Typically, no. On most of the hangers I've seen, the screw is redundant. If it falls out, the skewer or axle nut will keep the hanger attached to the frame. If the skewer or axle nut comes loose, you've got worse problems.

You can use a little lube on the threads but also important is to remember to periodically check and make sure the bolt/bolts stay tght. As Jeff Wills said earlier that the R/D hanger will not just fall off if the bolt/bolts come loose. You also might want to check the R/D hanger and make sure it properly aligns the rear derailleurs so that the derailleur shifts properly. Your R/D hanger wouldn't be the first one that wasn't straight from the factory.

The hanger is still attached to the frame if the screw fails but it may allow the derailleur to go into the spokes. Loctite them ****s in and forget about it.