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That is not Echeveria (but often confused with it), it is Sempervivum.

Hanging over the rim is no problem with these plants. It could actually look very nice with many of them doing it :) If they grew toward one side of pot, it was probably side receiving best sunlight - and perhaps bit more water from rains? They are very hardy Alpine plants and typically grow in big patches (IMO, that is how they do and look best).

That is really big pot and quite deep. There is nothing wrong in keeping them there, but such deep pot hold way too much soil. These plants will grow even in vey minimal amounts of soil, or drape/crawl over bare rocks.

If you like the pot, you can use it. If mine, I would fill half or even more of it with empty, capped plastic bottles to take some space that is not needed for the plants. You could use upturned plastic pots, some ppl use packing Styrofoam peanuts and so on. That would make pot also lighter and easier to move if wanted.

Plants look quite OK, perhaps little thirsty but alright overall. To tidy them up, you can take all out of pot. Do not worry if any offsets fall off, that is normal.

Use same pot or different - it is up to you. Make fast draining soil mix: adding lots of perlite (up to half of total volume) will work well. Don't skimp on it, it helps drainage but just a little doesn't work.

You could take off all dried up leaves. Any offsets could grow on their own - I usually leave them unless they fall off. Your choice. They are attached to 'mother' plant by a stolon that is bit woodier and could be short or long. If separating offsets (referred to as 'chicks'), you can cut stolon to about 2 - 4cm and just stick it all the way into potting mix. They will eventually grow roots just from bottom of rosette. If you leave them attached, stolon will eventually withers. It is not needed for ever, I think of it as an 'umbilical cord' :)

You can pot them into few pots - there are quite a few plants and I am quite sure they will grow and multiply happily after repotting. They should be watered approx. 1x/week, unless it rains. Pls. do not overwater - I am just suggesting bit more often than they likely received before. It also depends on how well potting mix drains; if you let them sit in wet soil, they may rot - as other succulents would. You can always check the mix using bamboo skewer or chopstick, inserting it deep into pots. Bit more watering than they were receiving will help to keep them from drying too many leaves (some old leaves dry naturally, and that is OK).

They should do just fine in your location with morning sun. If part of any container doesn't receive enough sunlight, you should turn the pot - maybe 1/4 turn every 1-2 weeks or so. I keep mine in full sun, whole day long.

BTW, these are monocarpic plants - if a rosette blooms, it will die off after flowers are spent. That is normal, and plant will grow many offsets before to replace itself :)

Pls. ask should you have any further questions...