There are courses and books on cycling more safely in traffic. "Vehicular Cycling" SOme of this is counter-intuitive to how a person who is "scared" might ride, and they are well worth reading. Some simple things are avoiding "dooring" and the most common accident, a right hook by a car (passing you and turning right into your traffic right of way). Increasing your visibility to drivers, being aware of sun glare into driver's eyes, etc. ALso, cars often underestimate the speed of a bicycle. and "Taking the lane" when appropriate. There is also a forum on BFN on Safety and Advocacy. It is an intense and sometimes divisive forum, but you might check in there.

As far as falling, it is one of my least fears. I have only fallen a couple of times in 14 years and tens of thousands of miles. The crash pictures you see are rare and usually from someone going rather fast - though not always.

I use a Topeak "Road Morph" pump - one on each road bike - and it even has a pressure gauge. It will easily get to 120 psi. Around here, I can get a flat every week or so during "goathead" season. I got 5 goatheads last week on one ride.