You can have the same underlying asset on each pool. You are correct that priority of cash flow and which tranches take the hit (in cash of default) can be one of the factor determines the seniority of the tranches. Other factors can be quality of the underlying assets, level of collateral protections, side-letters
The pool is a homogenous cashflow asset. It’s unlikely for individual loans / assets split up and allocated to different tranches. I’ve not heard of it before.
The rating of each tranche is based on the credit enhancement; i.e., what level of subordination sit below you in the cap stack. The AAA may account for 70% of the stack, meaning you have 30% CE, the equity has 0 CE and is therefore first loss.
The cap stack tranching i.e. how much is AAA, AA, A, BBB, BB, NR is based on assumed default rate, loss severity (recovery), scheduled and unscheduled repayments.