What could I expect to pay for a mini split to be installed

The costs can vary a lot, even with a single zone system. Costs of the units themselves vary tremendously between brands, sizes, and capabilities. Electrical and plumbing (that condensate doesn't drain up hill so either it goes to the basement sump or you are able to to mount it high enough on the wall such that it can drain outside but you'll still want to route it away from the basement wall). I think you are just going to have to get quotes, the 2-zone system we did for the other house was $18k, Samsung and heat pump capable down to single-digit temps.

Depends on size, I’d say full installed cost anywhere from $2-4k. But you can easily install on yourself and have someone come and pull vacuum.

You might look at the DIY systems with the precharged line sets. In a basement I'd assume you would have to add a condensate pump. I'm set up to install any type of system but I was impressed at how easy it was to put in the EG4 2 ton system from signature solar.

9k diy system

I just paid $5500 for an 18k Mitsubishi installed in my garage.

I paid $650 last year for a system I provided all parts for to a tech after hours from my main AC company

I got quoted $7500.00 to install a 2ton unit. Found another guy who did it for $3200.00.