home_visit

Kyiv didn't have anything available in Aug 2020 when we tried to reschedule in July.  I emailed them and they said they had no available dates.  The first week of August we tried again, and 3 dates in August were available.  Back then, student visa applications had priority.
 
I assume the embassy has not refreshed or updated their appointment calendar and will probably not do so until they are close to finishing the DV applicants.
 

Wouldn't DV applications be handled by the Immigrant Visa unit?  NIV unit that handles B1/B2 would have separate staffing and scheduling, no?
 

Hello,
 
I think they may have frozen the appointment calendar to process DV applicants this month.  Wait until the end of the month or Oct 1 to see if slots are available.

I was in a similar situation as you, I was working and living abroad and only wanted my partner to return home to meet my family.  In three attempts I tried to use my links abroad (i.e. my employment) as an advantage for my partner, to show that we have no intention of staying in the US.  My partner told me they usually ignored the letter from me and my employer, but on the third attempt she succeeded.  In this third attempt we were living in a third country, i.e. she had become and expat herself and not a local, that may have been a factor.
 
Basically if you have $160 to spend then it's worth trying but it is usually a disappointment. 

Yes, she can get married in the US with tourist visa:
You can also submit I-130 during her US visit after the marriage: "The beneficiary will not apply for adjustment of status in the United States, but he or she will apply for an immigrant visa abroad at the U.S. Embassy or U.S. Consulate in"

It is just the tourist visas.  There are not any other real options for fiances or spouses for the US.  Getting a B2 for the purpose of visiting for a fiance or new spouse is extremely hard.  If you have residency in this southeast asia locale and have been married for a few years the odds of getting a B2 is a bit better.

Yes, get married on tourist visa and then go back home. 

You file the marriage notice 3 weeks before you want to get married.  Show up 3 days before and leave.  If the spouse's countries involved require something to be filed, like the Philippine's Report of Marriage, you stay an extra day or two.
 
COVID quarantine is a whole different issue.
 
There is no benefit to getting a fiance or spousal visa if the intent is not to immigrate to the US.  Immigrant visas are for immigration.
 

Well, anyway, I was just chatting with a friend of mine (Cambodian) who had basically the exact same situation as mine, and on her application she said that her boyfriend would be paying for her trip, and she got a visa, twice. She said not to let people on this forum discourage you to much.
So far I haven't had much in the way of constructive suggestions but just a lot of mention that it's a slim chance.