Tesla seems to be pivoting towards the German Luxury model of car sales, where they lease them for 3 years and then sell them "CPO". I suspect, without running the numbers, that that will help with the profit(or loss)/unit situation.
The "make it up with volume" plan is more trying to sell enough cars that they can keep investors giving them money and stay solvent until the newer plants (Car and Battery) come online and lower manufacture costs. I don't know if it'll work, but it's not as stupid as just sell more cars at loss -> Profit. They are also building a plant in China, that will open a large Asian market.
It's also not as cut and dried as that. My understanding (and I can't find numbers right now) is that the Roadster is a revenue neutral or small loss flagship car for Tesla, like the Ford GT is for Ford. I don't know about the Model S, although Panasonic has lowered battery costs recently so they should be in the black.
This Article from 2018 puts the cost to manufacture a Model 3 at $28,000, and says they might not be profitable at $35,000. But we know now that the vast majority of Model 3's sold are the $50-$60k versions, which leaves some nice per unit profit. Whether that remains true as the US EV tax credits taper off we should know in the next 6 months. The Model Y is do out next year and is supposed to have economics similar to the 3.
I'm not a Tesla Fanboi by any stretch, but I am impressed by the cars they are turning out now compared to 5 or 6 years ago. We are a 3 vehicle household at Casa de Mush, and when the wife's 2015 Mazda is due for replacement in a couple years a lightly used Tesla is very much on the RADAR. As a second vehicle to commute into the city from the outskirts they make a lot of sense.
I haven't kept up on the SolarCity news so I can't really comment on that side of the OP, but I will also point out that SpaceX is pulling in a pretty damn healthy chunk of revenue from Falcon 9 these days, and the Dragon is on track to be operational next year. They can almost name their price to put people on the ISS at that point, especially as politics make the Soyuz less palatable.