To answer backwards-- first, your number 2 question:
If I'm understanding your question, the answer is "yes". Here's what happens-- the heel flap is done in that slip stitch thing to pull it in a bit, reinforce it a bit, and cushion it a bit. So on the right side you slip 1, K1 across, and on the wrong side, you purl everything (although usually you do slip the first stitch on the purl row, just to keep the edges of the flap even with each other). If you slipped the same sts on both right and wrong sides, those sts would never get worked and it would bunch up (vertically) something awful.
Now, for question number 1:
Pretty much yes, in a standard, nothin' fancy sock pattern, the sts should always be an even number. Here's why-- The legs of socks are almost always worked in an even number because they are usually ribbed at the top, or even sometimes the entire length of the leg. That works out better evenly-- although you could K3, P2 and do it for 9 repeats and therefore have 45 sts, for example. But it's most common to do it in an even number. The circumference of the foot is generally knit in the same amount of sts as the leg, and THAT should be even because when you come to the toe decreases, you want an identical number on the top of the foot and the bottom. Working the Slip 1/K1 pattern of the heel flap is easier worked over an even number of sts.
So what's the difference of 1 st, which is all it would take to change from an even to an odd number? Of course, pretty much nothing, when it comes to the size of the finished sock. But keeping track and making all the changes from leg to heel flap to turning the heel to the gusset to the foot to the toe just works far more easily with even numbers, and there's really no reason to do it differently. As I said, this is for basic socks. With lace patterns or other fancy work, there may be a need to use odd numbers of sts. I, however, have no experience with that, as I adhere to the school of thought that there is a limited view people are going to get of your socks, and if you're going to do something such as lace, then it should be at eye level where everyone can see it!