Tezos doesn't provide any randomness though Michelson currently. PVSS features are expected to come in future proposals which can enable randomness generation.
Currently, the best solution is probably to use an oracle(decentralized or not) to achieve the necessary randomness.
When you add tezAmount liquidity you deposit tezAmount * tokenPool / xtzPool tokens (with division rounding up) and receive tezAmount * lqtTotal / xtzPool LQT (with division rounding down). When you remove lqtAmount liquidity you get back lqtAmount * xtzPool / lqtTotal tez and lqtAmount * tokenPool / lqtTotal tokens (with divisions rounding down).
You wouldn't get meaningful privacy. It would be the only asset in its own pool, so you would know every time it changes hands, which might as well be achieved by using fresh keys without any zero-knowledge proofs. The multiasset pool would give you more meaningful privacy, but it's not a part of Edo.