Yes, you can do this!
I learned to do lots of DIY years ago and yes, I was middle aged. I made masses of mistakes, but since I was divorced at the time, there was no one to yell at me when I did so. Honestly, it's so empowering when you manage to do all this sort of thing yourself!!
I'm in my sixties now and do all my decorating/building/climbing ladders etc.
I'm sure you're in a better place than I was when I started....I had to get comfortable with a hammer, teach myself to use an electric drill and eventually an electric saw....now I can dismantle, paint, wallpaper, put up shelving and make up flat pack furniture properly. If I can, you certainly can....
Removing wallpaper....how bad is yours? Some can be pulled off and the walls just washed down. Check if it's an old house with disintegrating plaster underneath, you might have a flood a dust and have to fill with plaster in places. If it's a serious covering, you may have to hire a steamer....can be hired from B&Q or similar shop, works like a heavy steam iron across the wall and then wet wallpaper peels away. Can make your arms ache and fill the room with wetness, might want to ask a friend to help but doable on your own.
Painting is lovely, very relaxing and therapeutic. People swear by using rollers but I find them a nuisance, roller paint often needs more than one coat, splatters everywhere and leaves a "stippled" surface, but each to their own. I use brushes, can be useful if you need a very thick, even coat of paint and you learn to "work" the brush properly to produce such a surface. Woodwork requires gloss or satinwood paint and is an art so you don't get 'lines' in the finish...but again, very doable. If you want to be a perfectionist with woodwork, several coats with sanding in-between is the way to go.
Carpets are easy to pull up, there's always a massive mess underneath, think about where/how you are going to dispose of the unwanted carpet.
If I'm honest, the only thing I would baulk at doing myself is floor sanding. It is a heavy, noisy and intensely messy job. Needs machine hire and serious face-masking, there will be dust absolutely everywhere. If you can afford it, I would bring in a professional just to do that bit if at all possible.
Dismantling a wardrobe? Easy. Get yourself a claw hammer, and a decent set of screw drivers. If you are a novice (not sure if you are, apologies if not) dismantling furniture/fittings is the best way to learn how to put others back together again, as you can understand how complicated joints and hinges work (fitted kitchen cupboards is one example of this).
Go for it, and congratulations on your purchase!