One way to look for different environments is to replace (for instance) the each hydrogens with a dummy element X, and see if you have different compounds as a result.
So how may are there in propane? CH2XCH2CH3, CH3CHXCH3, CH3CH2CH2X (but this last one is the same as the first), so there are only two environments here.
How many in propan-1-ol (your second structure)?
Your second question is a little more involved. Typically, if the environments are the same, then n protons will split your signal into n+1 peaks, but if they're different, then each will theorectically split in it's own right - but you may not be able to see each of the individual peaks.
So in propane (again), the methyl protons (on the end) see the methylene (in the middle), and as there are 2 methylene, you observe a triplet. Similarly, each of the methylene protons sees 6 methyl protons, and you should be able to see a septet, but here the end peaks are relatively weak - do you know about the actual intensities of the splitting pattern - so you may not see them.
At one level, if for instance you had 1-bromopropane, the situation is similar for the 3-methyl, and the 1-methylene - both splitting into a triplet, but as the two neighbouring environments for the 2-methylene are different, you might observe a quartet of triplets (or vice versa) but the J-values may be very close, so you might not get resolved peaks