Does a crypto exchange website need to run its ethereum node?

hi, there. I am learning about ethereum-based crypto exchanges, and I tend to 'scratch my head' often.

Does a crypto exchange website need to run its ethereum node? (Is it necessary for the ethereum server to sync all the blocks?)

or a crypto exchange need to store all ethereum network data and run an ethereum node, because that's how it interacts with EVM (facilitates transactions with the external accounts/wallets) (is it so?)

Does it mean a crypto exchange website needs to run its bitcoin node also?

Because running an ethereum node is not easy. I was just wondering, if all those crypto exchanges run their own ethereum nodes?

I am sorry, if my question sounds dumb. I am still learning