Google docs has no link to ads. I’ve never used the Google Calendar web interface. I just use it with the built in calendar app on iOS. Same with gmail. Rumors are that Youtube is barely at break even after all of these years.
As far as Android, it came out in the Oracle trial that it has made less than $40 billion in profit during its entire existence. Which isn’t nothing, but seeing that Google has close to 80% market share (not including AOSP based Android phones in China) is not really impressive.
You may be right with the apps, but Google is paying a lot Apple for providing the default search engine. It doesn't need to pay for being the default for Android (other companies pay Google for Play Sevices).
Mobile revenue is at this point bigger than desktop revenue, so Android and Chrome were really necessary projects for Google to not lose direct contact with users.
With youtube you're right, it took a lot of time to be slightly profitable, but I'm happy to pay for it monthly, as I'm learning a lot from youtube videos.
From what I can tell, OEMs didn’t have to pay for Google apps or Google Play Services but they had to place Google apps prominently and had to have Google search as the default search engine. It was also an all or nothing thing.
That changed recently because of an EU consent decree. At least in the EU. Now OEMs have to pay up to $40 per device.
Those numbers could have well come from advertising and Google Play. I couldn’t find anything about OEMs paying to license Google apps before the EU consent decree.