Will staff and people notice if I buy tickets to a hockey game upper sits and then once the game starts sit at the bottom?

It depends on the building/team. I can recall being invited to grab a better seat by security at a NHL game once. Presumably they had orders to make the crowd look less sparse for TV.

Depending on the area, they may care and check your tickets, sending you back up to the nosebleeds. Or, they might look the other way. I always sit low, but it seems the seat thieves are most successful in the third period

If you are in places where hockey doesn't matter, they prefer it. In Florida, Carolina, and Arizona itlooks better on TV when the lower bowl is full. In real hockey towns those seats aren't empty they are just not being used. In Toronto people in the lower bowl are actually watching the game in the lounge eating and drinking with their friends. Security will stop you.

Who really cares. Enjoy the game.

yes it depends on the staff though some let you stay if they see the seats were empty the first period

yes

No