Enough that they are really tenants and should be on the lease?

Lastly, have them sign a mini-lease with these details. 

We are waiting for our rental lease to end to buy our first property—hopefully a multifamily house hack (if we can find one that makes sense)!

Listing Price:$ 99,990Down Payment: 20% ($19,980) Closing cost: $5,100Loan balance: $79,920 @ 5% for 30 year termEXPENSES (Monthly):Principal & Interest: $ 429Vacancy $40Water/Sewage: $0Taxes $212Insurance $76.50Utilities: $0Management $144Maintenance $24Trash $0CAPEX $172.80TOTAL : $1,098INCOME (Monthly):Rent 1 bed 1 bath $800 (occupied on 1 year Lease)Rent 1 bed 1 bath $800 (occupied section 8 for past 10 years)TOTAL: $1,600I plan to offer about $87K to sweeten up my cash flow, considering they have already dropped the price before and seller is motivated due to acquiring this property from a deceased family member.

We found that flips with enough spread to make it worth it to us were getting harder to find so we switched our model to a lease option model and it has worked out well for us.

I used to rent rooms as well and would never recommend yearly leases for those situations nor would I ever recommend verbal leases in any situation.

I found out about the tenants section 8 status and current lease (which was just resigned on June 1) when I was touring the property.So with the current tenant, is there anything I need to watch out for or dig into?

They will likely also want copies or leases, info on tenants and an assignment of rents as protection. 

Is it easy to make a flexible lease to allow tenant to move out any time they want? 

If you do it without proper approval, and the lease requires it, you'd be violating the lease.