I asked that do we need to set a slab (for e.g.: if we need to take in transactions with fees not less than 200 sats/byte and not more than 600 sats/byte, do we need to (or can we) put it like 200 - 600 sats/byte transactions to include transactions within the mentioned slab only)?
Yes, you can include any transaction you want into your block.
A lot of people seem to not understand how a block is generated. Its not like you 'mine a block' and afterwards include your transactions into it.
I would suggest to read
https://en.bitcoin.it/wiki/Block_hashing_algorithm and
https://en.wikipedia.org/wiki/Merkle_tree.
As well, if this is the case and we are allowed to choose our own size of transaction according to the protocol and decide not to include those low-fee/byte transactions, will they ever confirm?
If those low-fee/byte transaction will never be mined, they never will confirm.
Its fully dependend IF and WHEN a miner decides to include this transaction into his block.
Im not sure what you exactly mean with 'we are allowed to choose our own size of transaction'.
Transactions can be up to 100kb in size (to be valid according to the network rules).