Telegram Premium is sold in defined periods; paying with ETH covers whichever period is selected at checkout. Whether that means paying again later or not depends entirely on the option chosen, not on the payment method.
Someone already paying for other things with a card keeps using that card for Premium too; someone already holding ETH can do the same with their existing wallet instead.
Reusing the same ETH wallet for Premium doesn't require a new address or setup beyond what's already used for other ETH payments.
Not in how it's paid — the checkout flow is the same; only the product selected changes, from a Stars amount to a Premium subscription.
Usually shortly after the ETH payment confirms on Ethereum Mainnet, similar to a Stars top-up.