I've done quite a few amino acid/peptide NMRs and visualization of the amine/amide protons is not always guaranteed. When you do see them, they are often gentle humps that are not well defined/split and do not integrate neatly to 1/2/3 protons. Most of my compounds were organic soluble enough that I could get them into CDCl3, but I don't know if there's a way to enhance the strength or splitting of those protons.
Yes, the environment does affect the shift. The amide protons I had showed up in the 5-6 ppm range and free amines more in the 2-3 ppm range (again, using CDCl3 as solvent).