1 and 2
Either the roof, or the windows and doors should be done first. The roof is a standalone item, nothing tying into that scope of work, except for the gutters, but they are still not part of that work that will tie into the progress. I would not do the gutters until the siding is done.
The logic for the windows is, since you know what the various layers are before the siding goes on, the window can be grounded out with an 2X perimeter before the new windows go back in. That way when the insulation layer goes in the exterior window trim will be in the proper plane for the siding to finish against. I am assuming the Hardie plank is 3/8" thick, 2 layers at the laps and the ground set in the area where the old window trim resided, leaving enough beyond the existing siding to butt the new insulation layer against. The window will be nailed into this 2X, giving it a solid mounting. A jamb extension will need to go on the inside. The rip of 2X can be adjusted to flush up with the insulation layer if needed.
3 Decks
If the decks are to be attached to the house, the ledger needs to be weathered (flashing set) into the side of the house before the siding is run. The deck should be through bolted into the box sill (rim joist, some call it). If it is going to be freestanding then the deck can wait
4 and 5
Added plumbing and outlets. In case the existing siding needs to be violated to install any of the outlets, or perhaps the hose bibs, though most likely not, it is good to get the location for the bibs mapped, holes drilled, just to be sure there will be no issues after the siding goes on.
6 Siding
This will be the time to inspect the exterior and make any repairs before it is covered up with siding or covered by gutters. All electric additions will be done and accommodations are made for the extra hose bibs, though not yet installed. They could be installed, it would mean a lap at the bib. Otherwise a clean hole can be drilled through the siding if it is waited on.
If you choose to freestand the decks, now is the time to get those going.
7 Gutters
Sound fascia, siding done to mount downspouts to, job done.
As a point to consider, if you go with vinyl siding, choose a good brand, go the extra mile. I have Wolverine brand, 6" beaded, solid color all the way through, thick, resembles painted cedar. I built the house in 1989. The siding is 22 years old, with yearly power washing it looks great still. I have never washed the whole house, just touched up areas where gutters are, and algae grows (the biggest offender on shady spots only).
Another point, the nailing of the siding will be made really difficult trying to go through the Hardie siding, think about removing it.
Last item, the roof does not need to be done at first, but it is a major expense as is many of the projects you are planning. If it suits you, the roof could be done at the end as well, it would be a matter of being careful of the gutters. I would not do it at the end, I just want to make a point that there is no other items that directly impact that scope of work.
I'm with your painter. It's like throwing out a pair of Allen Edmunds because there's a hole in the sole and replacing them with a pair of Timberlands.
Find out what it would cost to repair/replace the split boards. It'll probably be cheaper than redoing all the siding in a new/cheaper material. In addition you might lose some value in your home by removing the redwood siding.
Have the insulation contractors blow the insullation from the inside. Much easier to repair drywall and you don't have to worry about poor repairs causing water infiltration.
Maybe find a better contractor all together. Some people just do what they know and they may not be familiar with other materials and methods and they wind up talking you into paying more in time and meterials to do things their way.
I was just talking to someone the other day about their garage door. They used to have a very nice wooden garage door but when they got an automatic garage door opener installed they were talked into replacing the door with a poorly insulated metal one. Something about the opener not being able to handle the weight of the door. This was for a single car garage so that shouldn't have been the case. Anyway point is... This was many years ago and they still regret the decision.
Best Answer
Generically, that's called "Ship Lap" siding. What it is made of is another aspect; it could be wood such as cedar or redwood, it could be pressboard, it could be vinyl or even aluminum made to look like wood. You should be able to tell if it's vinyl or metal by tapping on it. If it's pressboard, you would be able, if you look long enough, to see repeating grain patterns, something that never happens with real wood.
That fascia / molding and the roof joint needs some professional attention in my opinion. That's a tough spot for a typical DYI project and getting it wrong can leave you with some serious water damage.