Everyday or every day?
(commonplace) is an adjective: Plunging the kitchen sink drain has become an everyday occurrence. Every day describes the frequency with which something occurs: I miss her more every day.
Anytime or any time?
Use anytime if you could substitute whenever: You can borrow my snow blower anytime you need it. Use any time when you mean any amount of time: If you have any time Saturday morning, I'd appreciate some help in the garden.
Anyone or any one?
Use anyone if you could substitute anybody: Does anyone have change for a twenty? Otherwise, use any one: Any one of these chairs will look good in the lounge.
Everyone or every one?
Use everyone if you could substitute everybody: Is everyone ready to hit the road? Otherwise, use every one: Every one of these recipes will work for your reception.
Altogether or all together?
means in total: Prior to summer vacation there were nine of us altogether in the string ensemble. I was altogether pleased with our performance. All together means all at once or all in the same place: Last year was the first time we had been all together since 2008.
Anymore or any more?
Use anymore if you mean if you mean nowadays or any longer: You don't see that kind of attention to detail anymore. Use any more if you mean any additional: We surely do not need any more cheese until next week.