Any installer of these systems can answer all of these questions for you. Give them a call. By the way, the situation you describe is why most systems use ducts. You need to put the cold air where the heat loss is.

I installed three ductless minisplits in my 1928 Spanish revival. 2 9000btu units from Soleus were terrific. very effective, virtually silent, energy efficient, and included heat sinks. The other unit, a 15kbtu by an Egyptian manuft. sold by a Michigan company I have since blocked from my memory (house burnt down) was horrible. noisy and unreliable.

Brand matters, but if you get a good one, these puppies are a beautiful solution. They've been in use around the world for 30 years, so the tech is very mature. My 2-story house would have cost $15k to do central (2 separate units needed). I got all three installed for less than $4k.

Lessons learned:
1) you need a utility wall to install them. the outside line set is a bit unsightly, even if you install metal flashings over it. Think about your line runs carefully.

2) units are fairly inexpensive, but you must factor in the costs of the line sets (an AC guy can wire and pipe it himself, but it's somewhat easier and ultimate more economical to buy the pre-insulated line sets)

3) Make sure your installer has installed them before. they are not obvious (though they are simple), and experience goes a long way toward getting a good looking result.

4) they need power.

5) usually, you install a unit per room. this is actually cheaper and better than the so-called 2-zone units, which rum more than 2x the price of ingle units. the downside is that you will have a small farm of outside condenser units, so think about where you are going to stash them.

6) units are cheap, but install is not. Even if you do the line run yourself (not complex), they will charge you money to "charge" the units, usually an amount far in excess of what you think it takes to do 30 minutes worth of work. Hey, a guy's gotta get paid, right? Call around for bids.