1. treadmill is a piece of equipment in gym OR in the gym?
--- "A treadmill is a piece of equipment in the gym"
2. do you use the word "treadmill" or "running machine" to describe that kind of equipment
--- here, we use "treadmill"
3. Because "equipment" means all kinds of tools you can use in a gym, so is it correct to say :
3.1a kind of equipment to replace a piece of equipment?
---Did you mean "replace a piece of equipment with a different kind of equipment"
3.2 all kinds of equipment
--- this is correct