can they pick any valid transactions with significantly low fee?
They sure can, most people think no pool does that, but that's not the case, some pools do, a great example is ViaBTC pool which offers transaction accelerator services, they would include transactions that pay very low fees in return for a good payment directly to their wallet outside of the pool accounting.
Example:
The current fee is 1$, someone (usually by mistake ) pays 1 cent and their transaction is now stuck, they need it confirmed ASAP, they would pay $10 directly to the pool, and the pool will drop a $1 transaction and include the 1 cent transaction instead, the pool loses 4% of 0.9$ (the fees they collect from the miners), but they keep $10 to themselves, the miners, on the other hand, lose 96% of 0.9$.
i guess if it's an automated process, miner can't pick low fee transaction at all but i read that miners can include any transactions they want for the candidate block.
It is automated, the software does that, you can modify the code however you like, you can have your friend's transactions included regardless of fees, you can simply choose not to include any transaction in the block, and you can even include invalid transactions and lose a whole block, you can do just about anything you want since the code is under your control as a pool operator, but just because you "can" doesn't mean you would, it's all about profit.