Why not take the cistern to a decent plumbers merchant who can supply one that fits.
A flush valve is usually operated by a flush button ,but you can get lever operated ones. A siphon is what you have.
Is the WC close coupled ,or is there a flush pipe ?
You should take the original float valve to a decent plumbers merchant and source a new one with a suitable length tail,and forget the faffing about with washers. Also take the seal from the isolation valve ,and get a suitable replacement.
The thread of the valve tail in your picture looks like 1/2inch BSP to me.
The 15mm measurement in the pdf drawing would appear to be nonsense, having never seen a float valve thread with a 15mm diameter, as it appears to depict.
Your measurement of the threaded tail doesn't include the thickness of the cistern or the seal inside the cistern.
You will very likely find that your new valve will fit without needing to cut it at all.
There will be a seal between the isolation valve and the threaded tail of the valve,and you...
As above ,you will likely need to extend the pipework.
A TRV with a union fitting ,rather than the compression fitting yours has, may allow you to fit it without amending pipework.
Just turn the black handle ,the pressure gauge next to it should register the pressure. If the boiler error message doesn't clear and the boiler start to function,you would need to use the dial to reset.
Some of the copper conductors are sticking out from the terminals ,there should be no visible copper.
The red wire is hanging out of its terminal.
You shouldn't unscrew the switch plate from the mounting box with the power on either !
Push the seal back into the boss ,see if it is then watertight/ free of leakage.
If it is the white waste pipe needs support to prevent it from pulling outward from the boss.