Does bad/weak GPS signal affect battery life? For instance, when in the city downtown with lots of tall buildings or in the woods or mountains, will running GPS drain the battery faster?
No. Bad cellphone coverage decreases battery life because the phone has to transmit with more power to be able to communicate back to the cell tower. It's like when you can barely hear someone hollering at you: you shout louder too to make sure they can hear you. But GPS is a one-way signal: the phone only receives it, it doesn't transmit anything. It doesn't matter how much attenuation there is: either the phone can hear or it can't.
The only way a weak GPS signal would cause more power use is if you leave the screen turned on waiting for an app to get a position fix :-)
GPS generally affects battery life significantly only when used (in standby, its energy consumption is neglible, usually far below 1 mW). But when it tries to aquire a fix (i.e. you want to know your current position), it might reach consumption values comparable to your device's screen (~500 mW).
So in your described situation, it might influence battery life. But the "if" and the "how much" depends on how often apps try to aquire a fix. While this usually is done in foreground (i.e. you actively trigger it), there might well be apps using it in background, such as e.g. Location Reminders.
GPS eat up battery, as described in How much does “GPSing” drain the battery?. But I have no clue is poor GPS reception decreases battery significantly. And I also read this somewhere:
GPS only takes up battery life when something uses the fine position permission.
However, it drains more battery if you allow the GPS to be assisted by your network provider. In the Samsung Galaxy S4, this is found in
System settings > More > Location Services > Use wireless networks. It will use network information to make GPS location even more accurate based on network cell sites that are found nearby. And if network is poor (e.g. 1-bar signal), the phone works harder and drains more power.
I'll neither say yes or a no to this question. :)
Debateable - if you're acquiring a GPS fix through Wifi, you will not get it in the woods or mountains :)
However, if pulling 3G data across in order to acquire a fix, the question then steps in, how much battery juice is eaten up when trying to get a good "proper" signal (in between switching masts to get a better signal threshold) etc. (This ties in with @Dan's answer here)
Don't forget some apps will attempt to get a location as well Facebook is one example of such app.
Depends on what apps installed that have location permission, and as well as for services running in the background, all of these, will inevitably, slurp juice trying to run to obtain a GPS fix. So user bias can come in there as well.
One handset with just Maps will claim its fast, another handset with Facebook, Maps, G+, FourSquared will claim its slow.