Yes, you really have to do dig into it as there's a lot of information and a lot of different settings. As far as your Gerber Baby scenario, from my understanding this is exactly how it works. Assuming you're using Gmail for mail and you're logged into your Google account while performing those searches.
On Android you don't have to be signed into each Google App in order to use it, I'm not going to state that they aren't somehow connecting my device ID to my account information, but when I check my account history I don't see things showing up there. So while they could be doing that it isn't apparent to me and I also use an ad-blocker so I don't see ads when I'm browsing. Thanks for pointing out the information about the Google analytics, I don't have any sort of app or browser add-on that shows information such as that. It seems that it's inevitable that sites want to track their users and they utilize Google's free option to do so. But this doesn't matter what device you're using, it seems like utilizing a VPN + ad-blocker is probably the recommended way to browse the internet these days. But at that point, you're then trusting the VPN service you're subscribing to that they aren't logging your data.
I understand your point about Google using the user as a product to the advertisers and that's how they can provide their apps for free to end-users. But, Apple does provide a lot of free apps as well. For example if you go here:
http://www.apple.com/iphone-7/specs/ then "Free Apps from Apple" it lists: iMovie, Pages, Keynote, Numbers, and GarageBand (as well as other apps). If I'm not mistaken didn't these apps used to cost at some point? How is Apple now able to provide these for free? Also, once again, you nor I truly know what exactly it is that they are doing with the data from their users. Apple is such a closed system and proprietary so you're basing it off of what Tim Cook says in interviews and what is written on Apple's privacy section of their website. It is just more widely accepted that Apple is more trustworthy than Google.
I think it's about picking your level of comfort. Using Google who is much more open about what they collect and how they use it, or trusting Apple which isn't very open. I don't like the fact that these companies have access to all of this information from me, but I can't exactly go out and develop products of my own and a cloud infrastructure that works as well as either Google's or Apple's so I'm stuck with using one of them, or both.