The first two primary drives were there when I first bought my PC - "System reserved" and "Diagnostics",
The first partition is probably about 100 MB, and is used for booting Windows 7
The other is probably the recovery partition of about 5 to 10 GB.
I would like to know what would happen to my logical drives if I reinstalled Windows or installed Linux on C:, with/without formatting C: first.
As long as you specify the existing primary partition as the target, then nothing would happen to any other partition, logical or primary. A proper installation of an OS should only affect the one primary partition that it is installed in. No other partitions should be affected. But if you start using the partition editor that is available in most OS installers, then all bets are off; you could easily delete (almost) any partition.
Would they still be accessible even if they were created in Win7?
Yes. Linux would require a (simple) mount operation (similar to a removable drive).
If one of the logical drives failed, or somehow became unaccesible, would it affect the other logical drive?
Very, very unlikely, but remotely possible. The location and definition of each logical partition is based on the physically preceding logical partition. So if somehow the first partition's definition block got clobbered, then access to the second logical partition might be questionable. But this rarely happens. You can format each logical partition without affecting any other partition.