unfortunately, DEX in testnets such as BSC are non existent to test out trading taxes which will be prompted only in trading on dexes with liquidities.
so is there a thread or tutorial on which you can deploy your own local DEX via hardhat or live testnet?
This is not true. You can use pancakeswap testnet router
I assume this is the correct one on BSC testnet
Pancake Router :
0x9Ac64Cc6e4415144C455BD8E4837Fea55603e5c3
Which website can we interact with that? does it have any?
No that one is a forked version. This is the official v2 0xd99d1c33f9fc3444f8101754abc46c52416550d1