I would like to convert from 21 to 7 speeds.

This would obviously mean taking the front 2 sprockets off and taking the front derailer off as well.

Is this even possible and if so(?) what tools are required?

I have seen where some front sprockets are welded on. I assume these are impossible to remove?

A few things, you might want a different crankset and bottom bracket but if not here's my suggestion: Check your chainline and see which ring if any is centered to the middle of the cassette or freewheel on your bike, that's where you want your chainring you'll be leaving, if you're not going to leave the FD, use a chainguard, or a bashguard I'd make damn sure my RD tension was very good since that's what you're going to be relying on solely to keep the chain on your bike. You might find moving a larger ring to an inner position rubs the frame etc etc etc.. is this a nice bike you want to try this on or something you can learn from mistakes with? I also don't know your experience level, but judging by the question I suspect it's not much?

I have a 1x7 drivetrain on my commuting bike and am very happy with it.
Easiest thing for you to do is remove the inner and outer chainring from your current crankset; the middle chainring is probably lined up fairly well with the rear gears already.
You could leave the front derailer on the bike and just move the adjustment screws so it stays in place around the middle chainring, to keep the chain from dropping. But you're likely fine without it.

If your crankset has chainrings riveted on, then you might want to switch to a different crankset.

I use a guard in place of the outer chainring, so shoelaces don't get in the chain. But again, this is my commuting bike that I ride with everyday clothing.

Dig that bike my fellow 7 speed heathen.

Of course it's possible but to advise you we need to know what you want to accomplish by going down to 7 speeds, and which combos (front/rear) do you use now? We need pics of the left side of the bottom bracket to tell you what tools are needed. It does not matter if some are riveted (not welded) together, just if yours are. If so then you would either need a new cranset and possibly bottom bracket. Or no matter what you have you could just leave the front derailleur in one position. I would recommend that anyway to start, just to see if it's going to work.

It's a piece of cake. I bought a new crankset, and replaced the bottom bracket while I was at it. It need to be slightly longer if I recall correctly.

I wound up needing to fashion a chain restraint out of an piece of aluminum and cable clamp, where the front derailleur was. Those can be purchased, but all with exorbitant prices in my opinion, especially since a cheap DR would work better for a fraction of the price. So it may be (and simplest) that you'd just leave the DR where it is already.

Triple in the front? keep the middle one , take off the other 2 .. you may have to remove the crankarm,

to get the little one off ..

easy way ... just leave it on the middle gear...