I REALLY don't like doing things twice ...
This might indicate it is not a DIY project for you. However, if you are willing to do a few bits and pieces twice, you might be able to master the work well enough for a permanent result.
I also hate paying 3-4x more for someone else to do it.
This is often the best motivator, and hopefully provides some perspective. If you end up spending 20% more than a perfectly executed DIY, you are still way ahead.
1, should I do it (hardy) or the cedar
Dunno without seeing it. My house is brick on one face (the north side, oddly) and cedar shingles on the other sides. As long as the finished product looks like it is supposed to be that way, it should be fine. Have you thought about planting shade trees on the south side?
As far as redoing the siding's cladding/sheathing, you probably won't know until after tearing off the siding. It could be that part was well done. I don't think it needs exterior rating because it should be well protected and never in contact with moisture. 1/2 inch plywood or chipboard is standard, but thicker won't hurt and will help a bit with sound insulation and overall durability.
As far as house wrap, brace yourself: it is surprisingly expensive (maybe $100 for one side). If airflow through the wall is a significant factor, like all the other walls are tight and this wall is the big leaker, then it is worth it. If all the other walls and windows leak significantly, then don't bother unless you plan to eventually seal them all.
You might also consider adding additional insulation while that is open, both inside the wall cavity and perhaps as another layer on the outside. This might cost thousands, but given the high price of electricity there and typical air conditioning use, it probably will pay for itself in 8–15 years, as well as being a big improvement in comfort.
If you are going to replace windows, it will be way easier with the siding off than at any other time. The flanges are screwed into the cladding from outside. 14 years isn't all that old of a window, and a straight replacement isn't likely to save much. However, an upgraded replacement could well save on energy costs. Again the pay-for-itself period is probably in the 8–15 year range. Get an energy audit from your local utility (usually free) to learn more.
Hardness is a good way to check wood for damage without pulling it apart. Take a nail and press it into the wood where you know the siding is in good shape. Then, do the same where you suspect damage. If the wood is softer, then you can assume it has some amount of water damage. If you want a more direct, verifiable method your best bet is to yank a shingle or two off and check behind them. (From the pictures it looks like you have shake but its hard to tell.)
Also, as Steven commented...remove those "gutters" as soon as is humanly possible and replace them with actual gutters. Each year you wait things will get exponentially worse. If there is not currently water damage (which I doubt, sorry) there will be very soon.
Best Answer
Set the depth of the blade on your circular saw to be just deep enough to cut through the siding. Err on the side of slightly too shallow, and come back with a chisel, utility knife, or handsaw to finish.
If your circular saw's base plate is not long enough to sit across two planks of siding, you could fashion a jig to hold it. The jig could have a long base so it sat across 3 or 4 planks of siding. The jig just needs to be a long piece of plywood with simple stops on the 4 sides; the stops would hold the saw's base plate in place.