First of all, $35 for 36 spokes is a reasonable price. I assume you'll be paying labor charges beyond that? If not, you've got a super sweet LBS.

Wearing out spokes in 4 years is suspicious to me. That really shouldn't happen with a well-build wheel made of quality parts. Perhaps the original spokes were just poor quality, or they don't fit he hub flange properly. Do they break right at the head, where they seat in the hub? If your LBS is replacing them with heavier gage spokes, maybe the wheel was built with 15g straight spokes and the hub flange is built for 14g spokes, resulting in loose spoke heads. Or maybe the hub flange is too narrow resulting in excess bend at the spoke elbow (that can be corrected with a tiny washer on each spoke head).

Your wheel is probably a 3-cross, as that's the way most 36-spoke wheels are laced. The first crossing happens almost within the hub flange, so you may not see it. If it's really 2-cross, then your spokes are at a high angle to the hub when they should be almost tangent, and that would stress them excessively.

"Once I broke two spokes and the wheel got all crooked so would that have done permanent damage?" No, that shouldn't cause permanent damage. A wheel should be all out of wack with a broken spoke or two. If it is really out of wack with all spokes in place, then the rim is probably bent. If it's close to straight with a missing spoke, the rim is probably bent.

If you want to be able to replace spokes on the rear wheel yourself, ask your LBS to show you how to remove the cassette. Then buy a cassette lockring tool, a chain whip, and a spoke wrench. With the cassette off, it's not hard to replace a spoke and re-tension it. Takes some practice to true up the wheel nicely, but it's not hard.