It's really really worth getting a bedside cot, or one you can convert (long term/lots of space option: any cotbed; easy option but expensive: proper co-sleeper cot; budget but still good option: any of the ikea cots with removable side.) This solves the space issue, the falling out issue, and means if you ever decide to have a drink, or have to take medication, you have a safe space to make sure the baby is in.
WRT covering/clothing, I had DS in october so can only advise on winter temperatures, but I just slept in long sleeve pyjamas, open at the front, had duvet up to my waist, and shared a cellular blanket with DS, which would have been folded so it was more than one layer. He wore a vest and a sleepsuit. If it was really cold I wore a dressing gown just on my top arm and sort of draped over me. I'd recommend having the heating on low overnight anyway and hang the bills!
It's so much easier to regulate their temperature when co sleeping, I find. Just keep a few spare blankets and things beside the bed, (The bedside cot also comes in handy for this!) and check your baby periodically with a finger down the back of their collar. If their neck/back feels cool, add another layer, if they are sweaty, remove one. Don't bother with the complicated charts and instructions, throw your room thermometer away and focus on whether the baby is too hot or cold.
It's worth knowing as well that skin to skin contact actually helps regulate your baby's temperature. Your skin temperature will vary by 1 degree depending on whether your baby is too hot or too cold, in order to warm or cool them and vying them back to the optimal temperature. The mother's body is actually more efficient at regulating an infant's temperature than an incubator.