1.Can I install linux and configure a couple of fast HDDs in RAID and can I
have the same performances as some
expensive storage solution?
No. I would at least go with a decent hardware raid controller (Adaptec is my bet). The mai nreason is that your Linux install sucks in tuning simply because it lacks optimized hardware. Namely: you can not safely use write back caching because if the power fails the discs may be bonkers. You CAN do so in an Adaptec 5805Z or a 5805 with BBU becasue if the power fails, the on board cache is safe (for some or longer time - the BBU runs 2 days, the Z model writes the data to a flash module). Technically, btw., this i still running Linux (on the controller).
2.How many CPUs do I need, motherboard, other?
Pretty irrelevant. You are not CPU bound unless you do compression. Any CPU should be enough, even an ATOM. Again, unless you do a lot more than just pass the streams through o the disc, you are not likely to have a CPU problem.
3.What is the best brand of HDDs for this?
Western Digital. More specific: Velociraptors, if you need decent performance for a decent price. The only 10k RPM drive short of a lot more expensive SAS drive. Depending on your IO need you could get away with larger and slower drives. This has to be tested and a lot depends on your coding.
Get a server from SuperMicro - 2 rack units high, place for 24 hard disc (2.5 form factor). Plenty of space to expand. I would possibly start with 8 discs in a RAID 10 configuration. Multiple cages can be slaved to each other. Requires a SAS RAID Controller (as the above mentioned Adaptecs).
4.Does water cooling exist for HDDs?
Yes, but it is totally irrelevant for server. This is mostly for osmoen emaking a silent PC with total watercooling and wanting to get rid of the HD heat without a fan.