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The nut broke off and had a small red ring/gasket between these connectors. I'm an noob but can follow instructions. Please give suggestions. Thanks
Below there is a water valve 
which may be used as an alternative if the above (cupper?) pipe is inconvenient to use.
So far, everyone giving recommendations has failed to mention a crucial detail - which really shows the danger of asking for instructions online from people who don’t know what they’re talking about.
Since the previous joints were soldered, the heat has affected the material properties of the copper, making it extremely soft. Simply cutting the pipe and slipping a new fitting over it without a pipe insert puts you at serious risk of the joint failing catastrophically.
Honestly, I’d just call a plumber. They’ll sort it out in an hour, and you won’t have to wake up in the middle of the night to the sound of your SharkBite flying off and water spraying everywhere.
What I’d do here is cut the pipe at the straight section. You might want to cut off an additional 10-15mm to compensate for the new fitting. Then, to get the pipe inserts to fit into both ends, use a deburring tool to remove the internal lip left by the pipe cutter.
Next, take the nut from a new brass union and slip it over the pipe before joining the two ends back together with a compression connector - don’t use SharkBites. Then just add a new (presumably) 1/2" fiber gasket between the union and the threaded part of your toilet seat(?) and tighten the connection.
The copper pipe itself appears to be 12 mm, so you’ll need a 12 mm compression fitting and a pipe inserts suitable for 12 mm copper or 15 mm PEX.
If it’s for a washing machine, you need a flexible hose instead - since the machine can move during the spin cycle, and a rigid pipe might bend or crack. Here in Finland, building code requires a shut-off valve and a one-way valve after the hose, and those need to be mounted to the wall. That means you’ll need a hammer drill, wall plugs, stainless screws, silicone caulk, and so on. And at that point, you’re already past the cost of hiring a plumber just in tools alone.
Thanks, I read what you wrote and made a few adjustments. Here is what I'm trying:
From left to right:
•Toilet tank connector. •G3/8" F connector to G1/2" M. •Fiber(?) Gasket. •1/2" (15×21mm) F threaded connector to 16mm multicouche compression connector. •The white pipe (=multicouche, 16mm). •Same connector as last. •Rubber gasket. •G1/2" threadded connector to 10mm compression fitting. •Cupper pipe 10mm water supply.
The cupper pipe changes width quite frequently, unfortunately. But I think here is a good spot.
Why a fiber gasket and not rubber, if I may ask? I have rubber in the compression fitting. This feels better? Idk. I hope to replace the multicouche compression fitting with a press compression instead, for durability. This multicouche type is popular in France.
I'm not familiar with the term "multicouche" but it seems like what we call a composite pipe so essentially aluminium pipe encased in plastic. I've never used compression fittings for that, only press fittings.
Few points that came to mind:
If I were you I'd probably ditch the multicouche section entirely and find one of these:
There are ones with both straight and angled heads as well as ones with internal and external threads as well as 12 - 15 - 18mm ends that you can use the same compression fittings as for copper pipes. Here you could replace the gasgets and everything between them with just a 1/2" to 1/2" hose. You may even find a 1/2" to 3/8" one that you could attach directly to the toilet tank.
Regarding the gaskets, rubber ones seal better against uneven surfaces but fibre can withstand more heat and pressure. Rubber ones are also easy to overtighten. Tighten those with hand only and then around half a spin with a wrench. Don't let it twist while tightening.
I think one of these would work for you.
Do those bite to copper?
Yes. Sharkbite connectors are great for fitting new and old plumbing together.
Oof. No simple replacement nut to toss on there, unfortunately.
What i'd do if it were mine:
hacksaw and careful cutting of the copper a couple inches above the valve to get rid of the copper tubing (nothing wrong with copper, just harder to work with)
fitting on the end of the copper to give it a usable end. Easiest would be a threaded hose connection, something like this
that lets one put a common washing machine hose from the end to the appliance. Flexible hoses reduce trouble from the machine being moved a little by people/vibration.
You should not use a hacksaw to cut copper pipe for a sharkbite fitting, because supposedly the main thing that causes those to fail is the rubber o ring being damaged from rough edges. It's worth paying the $20 for a pipe cutter to not have to worry about a leak.
You need to cut off the end of the pipe and get a new fitting there which mounts to the pipe and threads to the wall. Take measurements and photos of stuff and go ask from your local plumber for parts, in here we very rarely use soldered pipes and instead we have compressed fittings which are pretty simple to install (and also pretty easy to fuck up, so maybe look for a youtube-video or something if it's your first time).
I think moving farther down to a straight area and cutting there to add a compression fitting or union would work better.
Since either one would add length, it gives OP something to work with.
Buy a new fitting just like what's on there (only for the nut), and a compression coupler.
Cut the pipe say 6" above the valve, slide on the new nut. Attach nut finger tight.
Put compression coupler (without rings or nuts) on standing pipe, check needed length in pipe to fitting, cut as needed.
Now disconnect it all, setup compression fitting with rings and nuts ok both sides. Again finger tighten the new nut. Double check it all fits well, then tighten everything down.
This way you don't have to solder anything, let alone deal with that bend and fitting.
Not a lot of slack on that bend, gonna be a bitch and a half working on a new compression fitting and sealing it. Dog speed, OP
You're not wrong on that. Might be easier to get some new pipe and couple of fittings to make whole new line.