C is just an older (launching) version of the RB211 535. Less power than the E4. If you want to have more than 108 to MTOM it is only possible with the (more powerful) E4 version.
The C version was the only version available for the 757 when she came on the market in 1983. BA was a launching costumer and (for what reason) kept the C version for the first 40 odd airplanes, although the E4 engine was available from 1984 onwards. Most costumers decided to go for the E4. E4 was developed by RR after the P&W engine for the 757 was considered to be more fuel efficent. Well, E4 is not as fuel efficent but is considered to be more reliable and less noisy; hence, almost every costumer took E4 engines.
To my knowledge only around 40 757 carry the C engines. Almost all of them are now with DHL. Allegedly E4 engine are less stinky (prone to oil fume/smoke).
No, no difference from a conversion point of view. Can be done with both C and E4s. But E4s can normally be heavier. So if you need the range one should be better off with an E4 allowing 117to take off mass. However, there shouldn't be any C left there are not yet converted to freighters.