At 10 1/2 months, he needs to nap when his body needs to nap. He should not be restricted to one nap per day in child care. Some babies nap once and some need to nap three times a day. Depending on the schedule in care, is it possible for them to let him nod off during a morning walk if it is too difficult to let him take a normal nap? Sometimes a little power nap is all they need. My 14 month old was down to one nap per day but is going through a growth spurt and has been napping at least twice a day for several hours each time, waking up to eat and play for a little bit. If he cannot make it to a reasonable naptime, or is not able to make it through lunch, he needs that morning nap. My boys also seem to sleep better at night if they get a nap or two in during the day.
About sleeping...I have let my children sleep with a blanket since pretty young...we swaddled them as babies and then I keep one tucked low. By 10 1/2 months, you should be fine to let him have a blanket at night, but he probably won't keep it on. We put our little guy in a fleecey footed sleeper or two-piece long PJs with socks. He kicks off socks. They also make footed stretchy pants, which are nice at night. 72 degrees is very warm for a child's bedroom, but if he is used to it, it should be fine. We don't have a thermostat in our boys' room, so after they are sleeping, I do a last-minute kiss and feel fingers/cheeks and see how well regulated they are. If the little guy kicks off his socks and blanket and sleeps with his shirt hiked up and his belly is cold, I pull everything back in place and turn up the heat a bit. In 72 degrees, too, unless he gets cold easily, it probably wouldn't matter if he has a blanket or not. Overheating is worse for them, so err on the side of dressing him lighter. Good luck! Hope he starts getting enough naptime! :)