Is it safe to use barn wood indoors for furniture, trim, walls and ceilings?
Working with reclaimed wood presents a few unique challenges and concerns. It sounds like you're going to be using your stock in its raw form so I won't get  into milling etc. 

The first thing to watch out for is dust. Barn wood is impregnated with all sorts of nasty stuff including molds and animal dander (a carrier of tetanus). Dust masks are an absolute must and take special care to clean out any wounds and splinters you acquire because they will often get infected. 

Another issue is imbedded foreign objects. Hitting an old bolt with a skill saw is as dangerous to you as it is to your blade. Pick up a metal detecting wand ($40) and go over your parts before you make any cuts, you'll be amazed at the variety of shrapnel you collect.

Finally, finishing reclaimed wood is its own bag of problems. Most protective finishes don't really like to be applied over top of dirt and contaminates so be sure to start by wire brushing out the worst of the gunk and then apply a good sealer coat before finishing, or better yet use a penetrating oil like Penofin for a more natural look. Note that any finish will change the color of your patina. 

As far as insects are concerned, there is a spray that can be applied to the stock that can mitigate or eliminate the threat of transporting them into your house but it's probably best left to a professional to handle it. If you don't see any signs of activity (holes, larvae, etc. ) you might not have anything to worry about.