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Congrats on the free Egg and welcome aboard!
The length of time your Egg will cook on a load is dependent on a number of factors but particularly on the temp the you're cooking at, the amount of lump you load, and the density of the lump. If you fill up the Large into the fire ring with the BGE lump and say you cook at 250 you should probably be able to go for 13-16 hours on that load. With a denser lump you could probably go 20+ hours but I've never cooked anything for that long. However I have seen some who have done low and slow cooks on LBGEs in excess of 24 hours.
Fresh lump will burn longer than partially used lump but you should be fine to either mix the used with the new or just dump it on top of the new.
You shouldn't really need to pull out everything to clean often. I do that maybe 2-4 times a year on my Large and XL but I'm sure there are folks who do that less often and other folks who do it more often. I do usually clean it out pretty well (without removing the fire box or fire ring) before any long cooks.