Do you get staking rewards for BETH kept outside Binance's spot wallet?

Converted some ETH to BETH (Binance tokenized version of staked ETH https://academy.binance.com/en/articles/what-is-beth-and-how-to-use-it ).

If you simply leave BETH on your spot wallet, you receive daily distributions associated with the staked ETH in the Beacon chain.

For lack of a better term, I will refer to these as "regular BETH rewards" (please correct me if I'm wrong).

Now, I do have some doubts and I was hoping you guys could help me (sorry I couldn't find the answer on binance):

(1) Do you get ETH2.0 rewards if you withdraw your BETH, say, to a hardware wallet? In other words, do rewards associated with your BETH "follow" you, or do you have to keep it in binance?

(2) The article I linked to above mentions other "ways to use BETH", like providing liquidity for example. But again, I don't understand, is any yield you might generate in addition to the daily ETH 2.0 distributions? Or do you forgo the"regular" rewards to use BETH on pancake swap/yield aggregators/etc ?