You can't stake your BTC because the algorithm doesn't allow you to. So whatever staking option for bitcoin you can see in the market, it's more of a ponzi scheme. There are multiple companies who also offers you to create a deposit account with bitcoin and give you certain percentage of interest back. These are not driven by the bitcoin algorithm so there's no guarantee that you will get your money back at the end of the deposit period.
Also why is it that only some coins can be staked? What are the conditions for a coin to be eligible to be staked?
It all depends on the algorithm itself. If the developer of a coin wants to implement POS algorithm, you will be able to stake. For example, ETH is now a POW coin so you can mine it. But in 2022 (hopefully) they will be moving to POS mechanism, so you will be able to stake the coin and won't be able to mine it using your computing power.
And why are the returns on staking different on different exchanges? Is it simply due to difference in commission ,as logically the return on staking should be universally same depending upon the lock in period?
As said earlier, these kind of exchange staking of bitcoin is not controlled by the algorithm. These are centralized operations just similar to a bank deposit. So the exchanges have the liberty to fix their own interest rate. There's no one control it! Hope this explanation helps!