Should I power up my only mewto (44IV)?

Bummer. I'd wait for another trade opportunity or figure out where your local EX gyms are. In the meantime, Alakazam can fill any role you may have had planned for Mewtwo

Just trade for more Mewtwo until you get one above 70% at least, if not 80%.

Now that it's in your dex, it will cost significantly less to trade. Something like 1600 Stardust at the ultra friend level. You don't need to trade shiny for it, other legendaries should do. A lot of people have a plethora of Mewtwo.

I'd suggest you find a discord for the nearest big city to you, join there and add some friends who may be interested in trading mewtwo for stuff like dialga/palkia when they come out, by that point you'll be ultra friends and you can make the trades (assuming you'll start raiding).

Otherwise if you NEVER intend to raid, then why do you even need strong Pokemon outside of Machamp and say dragonite, to take gyms?

I'd trade for more mewtwo, theres bound to be people who have more than they'd like to given how long it's been a raid boss.

If I were you, I would hold off for now and wait for N to confirm what the bonus stage pokemon is going to be. If it was a mewtwo, then you could easily obtain a higher IV version and power up that one instead. If it wasn't a mewtwo, then you can think about this problem again.

No, just no, it will miss lots of breakpoints.

You can always try to get a better one. But let's suppose you never do. Then:
* As a generalist, Rayquaza can be even better than Mewtwo. If you don't have any Rayquaza, then even a bad Mewtwo is still the best generalist you're gonna get until at least the next legendary, so you can power it up.
* As a psychic/ghost specialist, even a bad Mewtwo is still far better than any other alternative, so you can power it up.
* As a fighting specialist, don't bother and use Machamps/Hariyamas.