Spotify's free tier has ads, just like radio; so they are getting paid for free users and the more they have the more ad revenue potential.
Yes and no. It's very well known that Spotify's ads don't even remotely cover the cost of licensing material for users. Heck even with ads + premium subscriptions Spotify has been completely unprofitable nearly every quarter of its existence, and still has been unprofitable every year of its existence.
Ads is not a viable business model for them, it exists as a trial to push people to premium subscriptions.
I agree, and that is the crux of their problem. Spotify free is good enough for most users, especially hen it is used like the old radio model for casual listening or when traveling. Spotify has the advantage of tailoring music to one's tastes,and not having to move up and down the die while traveling; so a few ads in exchange for what is essentially a customized radio experience means there is no compelling reason to upgrade.
Spotify's problem is, if they make the free experience so bad that upgrading is the only choice with them to get a good experience, I suspect many users will switch to another service or simply listen to music they already have. iPods, Android and iPhones have all made it easy to have your own radio station travel with you.