dna sequencing - Separating DNA Fragments by Gel Electrophoresis. Are all the strands for one size the same?

The answer to the part of your question concerned with average lengths of restriction fragments is: if the DNA molecule being digested is of random sequence, and is 50% GC/ 50% AT, then the probability of finding any given short sequence at any position is 1/4^N where N is the length of the short sequence. So, for example for a restriction enzyme with a 4-base recognition sequence such as AluI (AGCT) the probability is 1/256 and so the average length of an AluI fragment would be 256 bp. For an enzyme with a 6-base recognition sequence such as HindIII (AAGCTT) the corresponding number is 4096 bp. Please note that this is the average length, and is not an 'expected' length.

The answer to the part of your question about fragments of the same size co-migrating, how would you purify them on a gel for further analysis is trickier. I think the first thing to say is that you wouldn't do this for sequencing, and this is reflected in the various answers you have already received - sequencing no longer requires this sort of approach.

If you were forced into this position for some reason then I can think of two things that could help: the first option would be to run the analysis on an acrylamide gel when you can get much better resolution of different fragments (all 50 bp fragments are not the same molecular weight), but this is really only useful for small fragments (100 bp or less). However the most likely way out of the co-migration problem would be to purify the two comigrating fragments as a mixture and then ligate them into a vector whereupon each recombinant would carry one or other of the two fragments. This is really going back to the original reason why molecular cloning revolutionised things - it allows the 'biological' purification of DNA fragments followed by production of these fragments in large amounts.

You mention "special base pairs that are lacking a hydroxyl group" so clearly you are thinking in terms of Sanger (dideoxy-) sequencing, in which case you could clone directly into an M13 phage vector so that you could make ssDNA for direct sequencing. By sequencing a number of clones you would find two sequences, one for each fragment. You would still have to find a way to decide which one was the fragment that you were actually interested in, however.

Like I say, things just aren't done in this way anymore.