Not quite. The thread of the isolation valve in your pic ( what the tap tail screws onto) is 1/2 inch BSP.
The washing machine / dishwasher hose thread is 3/4 inch BSP.
The Tee in your link is not correct. An equal Tee can be used but it would have to be fitted onto the copper,after the...
Is the problem radiator a vertical / designer type ,or a standard panel radiator ?
Given the fact that the problem rad heats fully when all others are closed off ,then there isn't anything wrong with it ,or it's valves. Close every other rads lockshield valve fully ,open the problem rads...
Is the leak only where the brass part screws into the chrome valve body ?
If so ,is the brass part fully tightened up ?
It should be fairly easy to make that joint watertight, if you are relatively confident on working on the plumbing.
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.