Pretty much anyone can demo a roof. Now it might take you a ton of time if you don't have the right tools but its not rocket science. There is a lot of trash so you need to get a dumpster.
Laying new felt or paper is pretty easy too. But at the same time this isn't something you would get charged a ton of money for and if a crew was doing your roof they might have it done in an hour if that.
Can you piece it over several weeks? Yea if you don't care about anything inside your house that could get flooded. Tarps aren't perfect and I have seen tarps blown and thousands of dollars of damage done.
What you are paying for when you hire a roofing company is the fact that they have expertise in installation, they know what materials to use, and they can do the job quick enough so there is no water damage. Do you know how to handle edges, drip panels, buying the proper nails/staples, knowing the proper installation pattern and techniques?
This is not the hardest thing in the world to do. But it does require expertise. If you are willing to learn you can do it by yourself. But the fact is if you make a mistake it will quickly cost you.
I have flipped a lot of houses. I will prep the roof area then let the pros take over. Could I install it myself? Yes. It is just one of those things that I don't do because of the cost/reward. I just had a new roof put on a flip. The roof was 30 squares and they did a ridge vent - pretty basic with architectural shingles. I demo'ed old roof and they charged me $1200 over material cost. There were 4 guys on the job for about 10 hours. Pretty sure they got paid about $150-200 a piece and company took the rest as profit.
Also to go deeper into your exact situation. You will need to buy something to cut the iron right. If cut wrong it will look shoddy. Nobody wants to buy a house where the roof looks half-assed. I am thinking you are looking at at least $300-500 in tool rentals and purchases (if done quickly). For gutters, these are only DIY if you can get long enough pieces to put up whole pieces and you have no corner joins.