Can I request retirement at my 20-year total time mark if I have 20 years of combined active and Reserve time? How does that impact Tricare?

You can collect that as long as You have 20 years of combined service but won't get any payment until You are age 60 You can get the Tricare but NOT the pay. wait the 3 years and collect right away from the active duty retirement. The amount of reserve pay also would be pro rated on amount as it measured by how many days of actual work vs active duty where ALL the days count to the maximum level and are NOT pro rated. In my opinion I don't think it would serve Yu very well to retire at this point with only three years to go for full active duty Retirement. If You went at 20 with 3 of those Reserves also You would be USAR (Ret) and could still be called back to active duty and not collect pay as opposed to USA (Ret) and collect right away and not have to wait. If You went now it would be Reserve Retirement which the years of active duty would add points to but it's a lot better to wait and do the 3 years active duty instead of going back into the Reserves which is what You would have to do.

You would have to transition back to the Guard or Reserve and the apply for a Reserve Retirement. That means you would get transferred to the Retired Reserve and not pull a pension until you are 60. I don't know the current rules on Tri-Care, other than it won't be an Army Paid insurance until after your 60th Birthday and you actually start pulling a check.
You get credit for any active duty time you pulled as a reservist, including AT, Active Duty Schools and any Deployments toward retirement time, you get credit for all your points toward pay. I would look to see where that put me. At the point you are at, my sage advice would be to suck it up and do the remaining time and to a regular retirement. You are almost at sanctuary now anyway.

It's 20 years of active duty time to qualify for an active duty retirement and the accompanying pension