Well, a bigger pot holds more soil and the soil holds the water. That can lead to rot, and you don't want that. By mixing perlite with your cactus soil, you can improve the odds of the plant not sitting in water. Mix 1 part soil to 1 part perlite and you'll have it cut 50%. I have my Aloe vera in an 8 inch orchid pot. I'm sure it was overpotted at first. But I have used a good draining mix for the plant and it stays outside all year. The top dressing of rocks helped hold it up until the roots took hold well. You can see the outer leaves are starting to yellow and die back, but the middle growth is still good.

Pic 4; wish I would know how to post multiple pictures at the same time. Aloe Vera ??

The pot size is adequate for now. Keep it in good light, a fair amount of sun although perhaps not during the middle/hottest part of the day. Water when the soil is completely dry.......this will vary with how much light it is getting, how warm it is, how big the plant is. The pups never have to be removed. If you want to later remove them to make new pots of plants you can do so but I would wait until they are somewhat larger than they are now. For now leave them. Remove it from the plastic and decorative basket. You will probably want a saucer underneath it. There are holes in the plastic pot to let excess water drain out and it needs to do so when watering so that water doesn't stay/sit in the soil. You are probably ok leaving it in that soil for now but when you do repot a grittier cactus mix would be better. Enjoy your new plant!

They're very adaptable. Probably just adjusting to the new soil. I'd leave it alone for several days and see if it regreens. Btw, the composted layer under chapparal is a great base for soil blending. Scrape off the leaves and take the granular layer. Add half as much real farm compost. How to find a real farm? Go to small town farmers' markets. Wofford Heights near Lake Isabella has a great one 9-1 Sats, at north end of town. Free coffee too, for a whatever donation. If in a big city, ask each seller if they are the farmer, and continue asking around until someone rings true. A real farmer can tell you how they compost their soil, feed their chickens, etc, and will eagerly tell you all about gardening. A fake seller will look away and say, No, he's around here somewhere.