I can't adress all of the problems, sorry.
But perhaps I can help with these-
(CONGRATS on getting it running though!!!!)
What do you mean by "doesn't stay flat"?
Is it warping due to the heater element, or skewing side to side or ??
If you mean that the leveling adjustments aren't staying in calibration, be sure to only use the four corner screws. Don't use the mid-edge ones too.
If you use all eight you'll never get it to be stable in my experience (don't ask me how I know that.....).
Some people only use three (two corners and the opposing middle) because three points mathematically defines a plane.
One of the very first things you will want to print is an improved Z-home switch and actuator tab.
The original one is horrible and if you even look at it funny it will slip.
Plus even if you clamp it almost to the point where it will snap, it will only relax over time and then slip.
There are multiple improved versions floating around, possibly being the single most popular "upgrade" for FT-5's.
Choose almost anything that does not rely upon clamping to the vertical guide rod.
Check on thingiverse.com
Some people do seem to have trouble getting the bed up to temperature.
Are you using the output from the controller board directly or through a current booster?
If using it directly, keep a fire extinguisher handy. Seriously.
Too much voltage and power loss through the connectors and on-board mosfet.
I have no trouble getting mine up past 100C (black bed version).
It takes a while, but it makes it eventually.
I do have an external current booster board though (minimal voltage losses).
As for the Z-steppers getting out of sync, you really, really, really need to sync them together mechanically.
Did I mention really?
Use a mono-belt approach like I have done (and Walter and others too), or add double motor pulleys and a third belt with a tensioner, again as others have done.
Parts for some of these are even posted on thingiverse.com
Mine just needs a 1350mm belt and four idlers.
No matter how you do it, this will solve the problem.
As long as they remain mechanically independent this is going to happen.
With my monobelt setup I don't even think about it because it isn't really possible.