I'm no more professionally qualified than you, but I do enjoy home improvement as a hobby and happen to know a bit about what you're asking. I've built a retaining wall the runs the length of my house and built a free standing deck with stairs at work.
1. Don't remove the wall unless you want a muddy pit. You might be able to throw some landscape fabric/mesh on the soil to keep it from washing away, but if the slope is extreme, I'd say wait until you know it's not gonna rain and you have a dedicated time to do it.
2. Lumber is relatively cheap. I wouldn't reuse existing lumber for many reasons, and the fact that it's cheap makes it that much easier to just replace instead of reusing it. Hardware stores have pre-cut stair patterned wood for less than $10 per run. You probably only need 2 of them for your stairs.
3. How tall is the retaining wall? If it's under 48", you just need to build it smartly. If it's over 48", you might consider hiring someone to do it, but you CAN do it yourself - it's just more involved. I can offer more specific advice once you've confirmed the height.
4. There are plenty of retaining wall materials that don't require mortar. In fact, I'm not sure that you'd want to use mortar because you actually want water to drain through the wall (as opposed to building up hydrostatic pressure behind the wall).
5. You can likely remove the stairs without destroying them. They're probably bolted on to your house/patio. You simply apply some WD40 on the nut holding the bolt and twist it off. You'll want to get a new set of nuts and bolts when you reattach the stairs. Reusing fasteners is typically a bad idea (and they're relatively cheap). Just take the old ones with you when you go to the hardware store to make sure you get the same size replacements.
6. Are the cinder blocks attached to the house? They're very brittle so you can easily hammer/chisel them away, but if they're load bearing you'll obviously want to get a jack to carry the load of whatever they're supporting before you do anything to further compromise them.
As for your concern of being underqualified, as far as I can tell this is a pretty straightforward project, though it does have quite a few parts. Those parts can probably be separated into smaller tasks that can be done independently so you can start and finish one within your constrained schedule.
Pictures would go a long way to providing more specific advice.
