"Pipes that deliver water are all hard, grey pipes with metal clamps"
This is polybutelene. Good stuff but the joints and chlorine did not like each other and the joints were often a different material than the pipes so leaks at joints were common. A big lawsuit put a lot of plumbers to work in mobile homes doing replacement. RV's, since they don't have the always on city water connection weren't part of the suit.
The replacement is PEX. you can get it color coded, even.
You can repair the grey stuff or the pex and even copper with Quest fittings or similar. These provide a standard half inch pipe fitting to standard 3/8 od tubing.
for some information and links. Lowe's is often a good source for PEX tubing and connectors. It also may be crimped (with special tools) for permanent fittings but occasional repairs in accessible places may find the Quest or similar fittings workable.