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

If you started off as Reserve or Guard and then went Active, your retirement time from Reserve/Guard doesn't transfer. You'll need another 3 years to retire from Active. Unless you want to go back to Reserve/Guard. But then....you'd have to wait some years before drawing pension. My advice is to wait the 3 more years to retire with Active Duty retirement and start drawing that check right away.

I would request verification that you indeed have the time. before requesting retirement. The "official letter" .I had a friend that did 3 active and 17 Reserves figured he had enough time and "retired" only to find he was 3 months short and they wouldn't let him back in to get it.

Don't forget the long game. IF you have 20 good years and can get on a Retired Reserve list, that just puts you into a holding pattern until age 60. Up to that point you get nothing so you'll need other income and insurance. TriCare is an option but so are others. I found it best to go with one of the FED programs as that was my CIV job. So now you're 60, then what? Unless you want to get highly variable service from VA depending on where you live, or don't want to be restricted to living near a MIL medical facility, the free TriCare standard is what you'll want. No sense in paying more to be required to get Mother May I's from the MIL side when your local Doc can refer away. All set right? Nope. When you turn 65, MEDICARE becomes your Primary. Part A (hospital) is free. You can get TriCare For Life for free, BUT, you have to pay for MEDICARE Part B (medical). Essentially TriCare becomes your MEDICARE Part D (drugs) and that's mostly it. Why? TriCare won't pay beyond what MEDICARE pays. So what comes out of pocket now? There's an increasing every year CoPay for drugs. For me in reality, that's mostly what I pay for. Express Scripts stuff just shows up in the mail and they are aggressive about hijacking prescriptions from your local pharmacy. OK for the everyday stuff, but when you need Oxy Whatever one time fill, make sure it's sent to your local pharmacy. I've had cancer treatments, back surgery, all sorts of labs, etc. and haven't had to whip the check book out except for some delta on MRIs and super sensitive lab work. Finally, if you make something of yourself, you'll be repetitively punished by MEDICARE with their IRMAA surcharges. That will mean that you'll pay ObamaCare high monthly prices based on your income two years prior. That said, life is better even if you are punished. Still gripes me that "medical for life" promises have been broken. As you age, the FEDs will continue to figure out ways to punish you more.

I am in this boat. I have about 10 years in the Guard with two periods in the Regular Army. Now that I am back in the Regular Army my time was adjusted. If you had any points that would have counted towards your retirement then they would have been added. So, if you had amassed 90 points in a reserve year they would be added to your active-duty service as 90 points which is pretty much 3 months. I hope this helps.

Yes you can pay for tricare prime, standard or any tricare. I had 22 years and I pay for tricare prime for my wife and I. I have it til I’m 65 then it becomes tricare for life

I was prior service as I returned after 4 years. They counted my inactive reserve time for pay purposes. I served a total 20 years active duty when I retired. As for my pay scale it shows 22 years.

Were you active duty then Reserve/NG then activated? I was active, got out then returned to active duty. I retired with 20+ years Active Army service but am paid for 22 (total was 23+ with reserve time) years. At the time (of course after 20 years active) I was told I could have retired the year before with 20 active - however things change so I would ask your S1 or call direct to Separations and Retirement Services.
Here's a couple of links:
https://militarypay.defense.gov/Pay/Retirement/ActiveDuty.aspx
https://www.hrc.army.mil/content/Separations%20and%20Retirement%20Services