Accidentally cut the bottom chord of truss

All the advice so far about ice damns is valid. However, if there are no dams or visible water on the roof, then you will need to crawl up in the attic and start looking for the wet areas that are wicking into your ceiling. The insulation may have been soaked before you got a chance to clear the roof. Obviously if wet insulation is found, it must be removed. Another problem I have come across in a few situations like yours, no dam, but slow moisture stains keep developing, came from improperly installed "proper vent" from the soffit vents to the air space in the attic. In a few cases, the open upper end of the proper vent was blocked or covered with insulation and condensation formed on the top side of the drywall right along the wall. In a couple of cases, no venting was used from the soffit and insulation was packed into this area instead. In either case, you will have to get up there and move the insulation in the affected areas and look for the moisture. Also look for any tell-tale water stains on the rafters or trusses that may have been a leak from above.

In order:

a) You can do it! You didn't mention anything about trying to move the existing structure, so this is based on my understanding that you are simply adding the tie back in to prevent further spreading. Personally I would use something more like a 2x8 or 2x10; a 20 ft. span is a long way for a 2x4, and you'll likely see some sag. I would put 5 nails into each rafter, in a rough square pattern with one in the center. But, you'll want to offset the nails a bit from each other so that they aren't going through the same grain (which can make it easier for a crack to split the wood where the nails are). You can cut the ends at the same angle as the rafters to get a longer surface to nail through.

b) If you do end up hiring someone else, a handyman could certainly handle it.

c) From your pictures, one tie every other is fine: the plates of the walls aren't going to move with a tie every 4 feet, and additional ones aren't going to do much.