Looks like it needs stronger wooden components all round - thicker uprights (telephone poles) and bigger cross-section members. You need to be careful how you deal with the base of the uprights too - if they just go straight into the ground they will, as you've seen, rot through.
My husband has built an open fronted implement shed totally by hand ie no power tools. He is currently putting up a large pole barn, although this time he has made the concession of using a battery powered drill. It is actually oversturdy to my mind as well as too large, but it shows it can be done, and by one somewhat decrepit person working on his own. He had no special skills for building but learnt as he went along.
So for your shed, it needs to come right down (lots of good firewood there) and a new one, whether wooden construction or metal kit, put up in its place.
You will though have plenty of other things to do when you buy your new land.
For help, if you have room in the house or have a caravan available, you could get HelpXers in - look them up, it can work well.