All EM waves undergo three physical phenomenons which are reflection, refraction (bending due to change in transmission medium), and diffraction (spreading after encountering an obstacle). Suppose you point a powerful dot-thin red laser beam at moon, ignore all the air and water particles etc. That dot-thin beam will become quite a huge size red spot after reaching the surface of moon. Because when the beam exits the aperture, it sees it an obstacle and starts spreading. Another very important phenomena related to an EM wave is that of ability of penetrating solids such as concrete etc. (check first four links)
This part seems spot on and accurate. Of course, penetrating simply means transparency. RF can go through concrete and light waves can't. This is independent of the line of sight issue, as you seem to understand.
To most people line-of-sight communication means that two communicating devices should be able to establish a direct communication path between them without any obstacle therein. For example, before Bluetooth technology became prevalent, infrared communication between two cell phones required that the infrared sensors of both phones should be able to see each other. But such an understanding of line-of-sight communication is not all correct.
The first part is my understanding of line-of-sight too, but you are correct to point out that terminology is rarely precise, and other meanings can come into play.
At this point also read through post #12 and #13 above, especially go through the links given in post #12. I believe both AM and FM are line-of-sight communications. AM signal can have global reach because of reflection from ionosphere. On the other hand, FM signal, which has higher frequency, doesn't reflect well from ionosphere and therefore has small range. If the earth were a plain surface which is to say no trees, building, mountains, air molecules, water particles, atmospheric layers etc. then you won't be able hear anything on your radio unless your radio and transmitting antenna can see each other. Because it would mean no reflection which play a dominant role if spreading of a signal. Q1: Do I have my understanding correct up to this point?
Here I would point out that the concept of line-of-sight with waves is a grey-scale not a black and white classification. You basically want to compare the wavelength with the dimensions of the obstacles. I think you will find that AM/FM is in the range where it is a mix of both line-of-sight and not line of sight, depending on the size of what's in the way. Obviously, AM would be less of a line-of-sight, than FM since FM has the higher frequency.
Infrared radiation has higher frequency range than that of AM and FM but it is comparatively bad at reflection etc. I'm saying this from my practical experience. Likewise, FM covers higher frequency range than AM and it is not as good at reflection as AM is.
I'm not sure why you mention reflection alone. Reflection and transmission go hand-in-hand and there are absorption/scattering effects and diffraction/refraction effects as you mentioned.
Infrared radiation covers quite a large range of wavelengths from 1 μm to 1 mm. That is similar to the RF range of 1 MHz to 1 GHz (I know the range is lower frequency too, but typically). Compare that with visible light which is 0.4 to 0.7 μm. Look at how the narrow visible range can display so many effects with color, reflection, refraction etc. So, IR with 3000 times more wavelength range will be hard to describe in general terms as far as comparing to RF with a similar >3000 times wavelength range. It would take a lot of research to really understand the comparisons, and I can't comment too much on this, since I haven't done the research.
Q2: Is there some relation between frequency and reflection?
Yes or course, but it is not simple. Various materials (conductors, dielectrics, and materials with complex conductivity/permittivity) would have very different characteristics. There is also strong dependence on incident angle. There are also absorption, scattering and other effects. Again I would say, think about what you see with visible light and all the variety with different materials.