"We are at the school now" is correct if you're describing your current location. It would be "We were at the school then/by then" because it is past tense.
By now means the act should have been done in the time before now, or will have been done.
For example, it's 9am and school starts at 8.45am. The mother says to the children, "Hurry up, you should be at school by now!" (as in you should have arrived before this time). In this sentence you could also use now (as in, you should be sitting in your classroom at this time).
The homework is due tomorrow, "You should have started that by now." You can't use now in this sentence, but you could say something like "You've got one night to do it so you'd better start now."
My friend left this morning to go on holiday "He'll be at the airport by now". I use by now because I'm not entirely sure but it's what the plan was. If I've just spoken to him on the phone I could say "He's at the airport now" - because he's told me and I know.
Another use I can think of is perhaps if you are describing something that has happened to you "I was waiting for the bus and it didn't turn up. Eventually a taxi drove up and by now it was dark so I thought I'd get it..." meaning that it became dark in the time between me starting to wait for the bus and the bus arriving. In this context, "we were at the school by now" could be correct, but "by then" would be more accurate in both cases because it's describing the past.
Hope that helps!