Your problem isn't the panel...
The panel you have is adequate for what you're doing -- swapping the circuit that makes up the bottom half of #9 to the slot below #6 (if worse comes to worse, just drop a BR115 in there as BR breakers are cross-listed to fit Challenger panels) will free up enough room for a two-pole breaker in the two bottom right slots, although this panel does not have much wiggle room indeed.
...but the size of your feeder
However, your condo's feeder is too small for the additional load posed by the electric car charger. Working through the article 220 procedure, we get 3000VA of lighting load (split across two circuits here), and then add to that a pretty healthy chunk of small appliance load (1500VA per small appliance branch circuit * 6 = 9000VA total) factored by the 35% demand factor for loads over 3000VA. Adding in the 18A air conditioner, we get almost 43A of load, before we add the car charger at 32A continuous, which puts us at 75A, well over the size of your 60A feed, and a good reason to have the feeder to your condo upgraded to 100A or 125A to go along with having a new panel installed.
As to until that point? You might be able to get away with running the car charger at night; however, I would keep an eye on your main breaker (which will be off outside your unit) -- if it trips, that's a sure-fire sign you'll need a service upgrade.
If you do put a new panel in...
If you do decide to have the panel upgraded, that 11" wide stud bay is quite the constraint; however, there are better options than putting in a 10 space panel and living with the space shortage, though, as you can take two or three of those narrow panels and daisy-chain them together using sub-feed lug blocks to extend the feeder down through two or three panel interiors and conduit nipples to connect the enclosures together. This lets you have oh, about 24 to 30 spaces at the cost of taking up most of that stud bay with panels and nipples, and needing to do some gymnastics to route wires out from the lower panels, but it may be worthwhile given the space constraints you are up against.
You may also be able to gain a couple of spaces by removing the main breakers from the BR1020B100F11 panels you're using -- they use a backfed BR breaker as their main, so if they have main lugs that are sitting fallow, I'd pull the main breaker out in that case and use the main lugs instead, in addition to the subfeed lug trick described above. (That way, you probably could get 30 spaces' worth of panel in your 11" wide space.)
