Can someone collect both a regular pension and a medical retirement? How will medically retiring early impact what I collect from the Army?

You're mixing a few apples and oranges together.

You can't "take a medical retirement" as it's not up to you. If your illness/injuries are such that you are medically incapable of performing certain functions of being a Soldier or of your MOS, then you'll be referred over for evaluation and processing through the IDES process (PEB, MEB, etc.).

Medical retirement from the military is all about if you can function as a service member and your ability to perform your military duty. VA disability pay is compensation on your decreased ability to perform work after leaving the military, impact to future health, etc.

As LTC (Join to see) stated, you can still be active in the military (reserve duty or active duty) with a VA rating - Federal law* prohibits you from being compensated by the federal government twice during the same period, which is why your VA pension is recouped (just a rough SWAG, but you'll get likely receive more money from your military pay per day than you will from the VA).

Regarding the collection of both VA Disability and a medical retirement from the military - Yes ... and No. If you are medically retired (Chapter 61), it's a possible "Yes" if you have 20+ years of creditable service, but a firm "No" if you do not.

There was a law change* that started about 20 years ago (2004) which implemented Concurrent Retirement and Disability Pay (CDRP) (the DFAS page that SP5 Peter Keane pointed you towards), but most individuals focus on "as long as you have a 50% or higher rating from the VA" part of it - mainly because they are longevity retirees (20+ years)*. Put plainly, CDRP doesn't apply if an individual has less than 20 years of service.

However, if you were medically retired and had less than 20 years of service, if any of the disabilities are combat related, then Combat-Related Special Compensation (CRSC)* may apply. CRSC is a program to add back compensation for those disabilities that were combat-related. Hypothetically, if you had two injuries that were deemed combat-related and they totaled to 30%, then 30% of the recoupment would be 'paid back' under the CRSC program. If you are eligible for CDRP, then effectively CRSC wouldn't apply as you'd already receive 100% of your VA pension.
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* 38 U.S. Code § 5304 (and 5305) - https://www.law.cornell.edu/uscode/text/38/5304
* 10 U.S. Code § 1414 - https://www.law.cornell.edu/uscode/text/10/1414
* Of the ~2 million retirees at the end of FY22, a bit over 133k were disability retirees, and only 29k of those disability retirees are collecting CDRP.
* VA CRSC - https://www.va.gov/resources/combat-related-special-compensation-crsc/

I know several reservists that are 100% VA that continue to drill, I know one on ADOS and I know of 100% VA soldiers being mobilized. VA ratings do not directly relate to service medical requirements so there is no automatic trigger for a medical separation.

You will need to do some math to determine if it makes sense to drill for points only or to drill for pay. The VA will back off 1/30th of a month's VA pay for each day of active service and each MUTA of drills. The question is are you paid more for a MUTA or for 1/30 of a month of VA pay at your rating Takoma in to account the tax advantages.

Yes if you medically retire you can collect both checks. If you do a traditional reserve retirement you can collect both as well but you have to wait until after the gray area.

To answer the last part of your question, if you stay until 20 and take a Reserve Retirement, #1 you can't collect until you are 60. There are some deployment deduction on retirement time, but I don't have that in front of me. 2. If you have 50% or over VA rating, you will pull a VA pension without penalty when your retirement pay starts.