(From a Linux geek still happy with a "dumbphone", but considering Android)
Can you use Android without serving yourself up to Google?
It is difficult, but possible. Just.
Is it true that you have to have a Google account to start up your phone?
No, but without a google account you cannot use their app store, and without an account of some sort somewhere you cannot use the calendar. I personally have setup a Zarafa server with Z-push to mimic an Exchange with active-sync. Using that allows me to use the calendar and sync my email, contacts and calendar without using google at all.
Can you (easily) install apps by just downloading them to your computer and then transferring to the phone?
That depends. If they are apps from someone who has realised that Google Play is not required, and just distributes the APKs then sure, easy as pie. If they are apps that are distributed solely via Google Play then, no, not easily.
You can however install them on another android device and use something like APK Extractor to copy them to install on your phone. I keep one of my old android phones for this purpose
Do you have to give up your credit card info and name/address to sign up for the Google app store? (In light of the recent story that app developers get all your info, I don't know if I want every 2-bit app to get that info. The info itself could be worth more than the 99 cents for the application.)
No. I haven't had to at least. I would warn you though that if Google have this information from another source (i.e. Google wallet or whatever they call it) I wouldn't put it past them to 'helpfully' fill it in for you
Also, do free apps also get your personal information?
Not to my knowledge. Only the paid app get your info afaik.
Any hints or links re: using Android without the all-seeing eye?
Builtin app replacement recommendations?
The first thing I tend to do with an android device is root it, and install a custom ROM. Typically Cyanogenmod, but sometimes others. I would recommend you have a good look to see which devices have the best developer community before you buy.
Second, if you don't have an exchange server available, set one up yourself on a machine you tend to leave on in your home network. That will provide most of the functionality you'd be missing by not having a google account tied to your phone. (If you are feeling adventurous you could set up a VPN and have secure access to this anywhere.
Apps wise, go grab one of the OpenStreetMap apps, which will have you covered for maps and route planning. Grab something like EStrong File manager so you can access network shares. And finally, grab something like ConnectBot, so you can ssh into your machines.
I think that pretty much covers my setup