Waterflow through vertical pex coils

I am trying to work out the practicaliites of running water through pex coils.  I have done this with them horizontal on a board, and had our boar water pump push water in one end and out the other and then run to an outdoor shower with a mixer with cold water.  It worked great for when the sun shone, but lost temperature as soon as the the sun stopped shinning on them, and we could get 15 min of guilt-free showers in summer for a number of years until the untreated ply rotted on the ground beneath them and the plastic film on top came off.     Now I am wanting to  stand them up vertically at the back of a greenhouse / side of our house and store heat in a water container below them.   I have two queries.

- If I have a small pump that will pump water from the container straight up to above the coil, will gravity and the leveling effect of water pressure allow the water to slowly run through the coil and down into the water box?

- Can Air locks form and what should I do to stop this?

Yes, this works fine as long as your pump's head rating covers the lift to the top of the coil. Once the loop is primed, water will happily run downhill through the coil back into the tank — the pump only needs to overcome the height difference, not the friction of the whole loop.

Air locks are the real nuisance here. Put a small manual bleed valve or just a tee with a cap at the highest point of the coil so trapped air can escape when you first fill it. Keep the coil pitched so it never dips and rises again mid-run — air collects in those dips. After the first prime, a closed loop with no leaks rarely re-traps air.

If you have a vertical coil, every loop will want to form an airlock. I think the best way to get around this would be to fill it while it is horizontal, close it off, and then lift it to the vertical position and secure it. A bleed valve at the beginning of the coil should help get rid of any air that finds its way into the coil, as long as it is not so much that it gets into the second or following loops.