Hedge maintenance in the first year/2

Just trim off a few inches of the taller ones, say 4 or 5 inches, and maybe two inches off the smaller ones. This will encourage them to spread by shortening the leaders. Also just pinch out the end bud on the sides of the bush. Next winter do the same again, by this time you should be able to do it with a hedge trimmer. Don't take too much off, just aim to take off the end buds. Eventually the bushes will catch up with each other and you will be able to trim the top to the height you want. But do keep light trimming in order to make it thicken up.

Since you want to keep it low, and beech is naturally a huge tree, you will have to really keep up with the trimming or it will look scalped.

Clip the hedge on the sides just enough to take out, on average, the growing tips.

If you're planning on a low hedge it's important to encourage as much branching as possible while the plants are still young. Trim back any long drooping or straggly branches to a point where they can support their own weight, ie to a point where they're 'springy'.

Also don't be afraid to reduce the height by 1/3 or 1/2 if there aren't many side branches

Nope do it now to get the full benefit of the seasons growth. It's not a good idea to trim or prune beech in winter as the cut stems can die back further especially if the ground is wet

Yes that's fine, cut back to an already emerging bud if possible

They'll do that, non green plants have less chlorophyll in the leaves so are less able to absorb nutrients, so are always slower growing.

In a mixed hedge the green will dominate the red over time

I'd also add keep weeds away from the base of the hedge. Feed in spring but now is fine. A "general purpose" fertilizer is whats recommended which tends to mean Growmore, blood fish and bone is also good. Don't over do the fertilizer and read the instructions maximum for growmore would be 2 oz to the square yard.