1. Theres a capped 15mm pipe under my bath by the taps, opposite end to radiator. How can I tell if this is a mains cold supply, other than sawing the end off and squirting water everywhere? (Its slightly warm to touch when heating is on, may be near a heating pipe below the floor? Hence why asking)
Could be a few things, I assume you can't trace it back?
If not, switch your mains water off and open you upstairs and downstairs cold taps. Also switch off the central heating pump. Pipe slice the end off and use a compression isolating valve. (make sure its closed)
Switch water back on and close taps, gently open the isolator and if you have lot of pressure it's probably a cold mains.
The slightly warm to the touch when heating is on suggests its a capped flow / return for the central heating. If its capped it wouldn't be able to flow so would heat via convection and not heat up as quickly as a rad.
2. Would the 22mm supply to the bath cold tap be direct or from a header tank?
It's likely to be a cold mains, not from header tank, but if you want to be sure go into the loft turn the big round red handled valve feed from the header to close it. See if you still get cold from the bath still if you do then it a mains cold.