How to choose a proper chromatography way to separate substrates? I'm a freshman and I recently learned how to do TLC and column chromatography. I also know a little about other ways to separate things by chromatography, such as affinity chromatography, gel chromatography, ion exchange chromatography, and gas chromatography, but without many details.

I am facing problems in solving a question requiring us to judge how to separate these combinations of substances by chromatography (if there was no such confinement, this will be much easier):


  
  N-phenylethanamide, N-phenylpropionamide
  methoxymethane, ethoxyethane
  Aβ36，Aβ42 (Aβ is a kind of peptide which is related to Alzheimer's disease, while the number, 36 and 42, refer to the amount of amino acids polymerized in the peptide)
  


Here are the specific issues I've met：


I've no idea how to deal with the first combination since their difference seems to not be significant, no matter in polarity, acidity (basicity), or molecular size. Is there any other chromatographic way, or did I get something wrong?
I think I can deal with the second combination by gas chromatography, since they are both volatile. But I'm not sure if it is a good idea. Is there a better way or not?
I've found some description for the separation of different Aβ, suggesting that the following ways are usually used: use antibodies (e.g. ELISA) or electrophoretic separation (e.g. PAGE). But seems that neither ways are related to chromatography. It is also said that reverse phase liquid chromatography after CNBr cleavage works, but this way is complex and time consuming. I'm wondering (a) if I can use antibodies or something else to deal with it by affinity chromatogrphy and (b) how CNBr works? (Now I know CNBr is used to cut proteins/peptides at where methionines are, but still not knowing how reverse phase liquid chromatography works.) Also I want to ask if there is a better way as well.
As you already mentioned, there are numerous types of chromatography, and they vary in several different ways. I can't tell you what would be best ways to separate each of these pair of substances, but I can give you some insights. Using chromatography always requires optimization of experimental procedures, and the first step is usually searching on papers and other references for information on how the specific separation is usually done.

N-phenylethanamide/N-phenylpropionamide and methoxymethane/ethoxyethane

Despite being very similar, the presence of one or two extra $\ce{CH2}$ group in each of the second molecules is enough to give the molecules different properties, specially considering they aren't big. For simple detection purposes, I'm sure it would be possible to find the appropriate solvent mixture to separate them using TLC or column chromatography. 

A much more advanced technique, gas chromatrography is very powerful and could also be used to separate them, as long as the appropriate setup was used (injection and oven temperatures w or w/o gradients, column type and length, etc). 

Aβ36/Aβ42 

These would probably decompose in elevated temperatures, so gas chromatography is not a good idea. Peptides are, nowadays, mostly separated using liquid chromatography, usually in HPLC or UPLC systems using reversed phase columns. This type of chromatography will separate the peptides mostly by their polarity and size, and once again, reference search and experimental trials are essential to optimize conditions. HPLC and UPLC are used to separate mixtures of thousands of peptides (with varying efficiency, of course), but that should be a sign that two wouldn't be a problem, even if very similar.

Depending on the objective of the separation (identification and/or recovery), using CNBr or any other digestion step could be useful or not, but I don't think this would be the case for only two peptides.

PAGE and the variations of electrophoresis were for a long time the goto separation method for peptides and proteins, but recent developments in chromatography (and mass spectrometry) have made them fall off preference. 

I'm not familiar with affinity chromatography (or the whole antibody thing, to be honest), so I can't say much about that, but, what I do know is that you won't always find or be able to manufacture the chromatographic column with the desired specificity.