I know that from the Blockchain alone the adresses can’t be connected, but i have some questions about this:
Are different crypto addresses completely separate in Trezor Suite?
When I start the Trezor Suite app, are all addresses automatically requested from the network or only when I click on an address?
Do all addresses use the same API key or other identifier when requesting their balance or sending transactions?
For privacy reasons, I want to prevent my addresses from being connected to each other.
Addresses are not requested anywhere. You can generate them in completely offline 
If they have zero balance, they will be forgotten, when you turn off your Trezor Suite. Of course if you create address next-time, same address will be created again = deterministic wallet (not random wallet 
).
As a privacy minimum - avoid sending back and forth (periodically) between your addresses.
But if i connect my device to the internet, then they balance get requested from the node.
And i can’t make transaction without connecting to the internet.
I know
If that is uncomfortable for you, you can always use TOR and your own Full node for greater privacy. Personally Trezor Company is my root of trust, allowing me to offload some tasks like assembling Trezor HW device from individual components, building firmware, building Trezor Suite wallet, running servers etc.
Did i run my own full node, Electrum Personal Server etc? Well yes, but mostly for educational purposes
For your own greater privacy in the Trezor Suite Desktop App - search Trezor learn portal page:
Full node via Electrum server
Privacy should be possible without running a node.
And that’s a reson why i buy Trezor (read Trezor’s privacy policy).
I hope Trezor make an option to disable automatic balances requests.
Still the same addresses go through the same IP, even if its a Tor IP