Nope. Even DDR-3 can perform sequential transfers at speeds well exceeding one byte per CPU clock cycle.
And yes, you can ignore the time to read from disk. Think a SAN over a 10-gig link. That gets you close to byte-per-cycle territory as well. It takes on the order of a dozen cycles (more or less depending on architecture and algorithm) to perform one "step" of a search. So yes, these algorithms very much matter.
Also, in modern x86 processors, an entire cache line (64 bytes) is read whenever a single byte is needed. So for strings smaller than 64, even algorithms that don't check every byte will read every byte from disk to RAM and from RAM to the processor cache.
Yep. But this is not necessarily the bottleneck; see my above comments about the CPU.