What would be the significance of being prone behind cover and not being prone? I don't see any real penalty for the former until the enemy initiates the assault.
The first question was about the sentence, "You cannot be both prone and behind cover" (p64, Players Manual) and the sentences, "If your CUF roll fails, you are suppressed. This means that you immediately drop prone, suffer 1 point of stress, and lose both actions on your next turn" (p67, Players Manual). If you were in partial cover around a tree, I had interpreted this as meaning you lost your partial cover, but this has now been cleared up. You are still in partial cover, you just don't benefit from the -1 modifier to attacks against you for being prone. This was quite important as without it being cleared up it looked like you had to first "get up" (fast action) and then "seek cover" (fast action) in order to get back to where you started before you were suppressed, i.e. in partial cover behind the tree. The sentence on p64 should really be reworded in an errata as, "If you are prone and behind cover, only the cover benefit applies - i.e. attacks against you ignore the -1 penalty".
The second question was about being suppressed when in partial cover behind a low wall. If you are suppressed in partial cover behind a low wall, you immediately drop prone (p67, Players Manual). You are now prone in full cover behind the low wall. You lose both actions of your next turn as you are suppressed. Now we are in a bit of a quandy as "go from full to partial cover" or "seek cover (full or partial)" are both fast actions - but so is "get up" (p56, Players Manual). The question is, can I go from full to partial cover when prone behind a low wall without first getting up? If I the answer is yes, then I can fire at the enemy the turn after I'm suppressed. If it's no, then they are safe from attack the turn after I'm suppressed, as the most I could do would be to get back into partial cover over the low wall (one fast action to get up, another to go from full to partial cover). Tomas of Free League said in a previous post, "it does make sense to allow a prone fighter to seek partial cover and get on their feet in same action, so I'd suggest allowing it".
To summarize...
1) You don't lose cover when you fall prone after a failed CUF roll.
2) When in cover and prone, ignore the -1 penalty to attacks against you for being prone.
3) Going from full to partial cover when prone behind low cover (barrier, boulder, etc.) includes a free "get up" fast action.