When I open "network map" on Tails, I see a list of IP addresses with locations. What are these? And it's titled "Relay". Does the government have access to all relay nodes on the TOR network as they are active? If they have a guess of a general location that someone is in can they use this info to track them down (like use data analysis to to get tell which one are they, like when they are active posting on a forum if they want to locate a particular poster and when that relay in TOR is on?)
Everyone has access to the IP address and metadata about all Tor nodes. This is unavoidable. In order for your Tor process to be able to randomly choose nodes, it needs to know a list of nodes in the first place. These nodes, along with their information (their "flags", their capabilities, what they are allowed to do, how fast they are, etc), are public information stored in a file called the consensus. This file is mirrored all around the Tor network, and it is one of the main reasons starting up Tor for the first time can take a while, because you need to download the whole consensus.
This is a short snippet of what the consensus looks like (the full thing is over 36,000 lines, so obviously I won't post it here, but it is public):
w Bandwidth=10700 r Unnamed DSKlNEqBZCDjk4inpj55237koBM 2016-04-03 13:36:16 22.214.171.124 9001 9030 m O9qPgH4mzyAink99kvRfXdq8w6NVtooV+w9zXdhadBU s Running Stable V2Dir Valid v Tor 0.2.8.1-alpha w Bandwidth=12 r csepelisland1 DSuQbBJIrpmIHZgFLvNR8EH6I20 2016-04-04 01:53:33 126.96.36.199 9001 0 m DHNRWHTyCgfbs9Z9g4QYh32CRApgiu11CdnpBzJrcAk s Exit Fast Running Valid v Tor 0.2.6.10 w Bandwidth=305 r tyriontornodepw DSycNQERJRfoJnpYZuAYJilAmrQ 2016-04-03 13:40:02 188.8.131.52 9090 0 m yf4cPoG1JoKSMVGwQQduIsedmywjhXhgWL7jQ2LfEjM s Fast Running Stable Valid v Tor 0.2.7.6 w Bandwidth=144 r HY100 DT66F+HHjx6ZALq9sjhh1G/K8WM 2016-04-04 03:09:42 184.108.40.206 443 80 m garu8wMlqR6wS3rm96EvsAvNlMIFOBoZWBcEXKeV0QA s Fast Guard HSDir Running Stable V2Dir Valid v Tor 0.2.7.6 w Bandwidth=20700 r OnionPi DUYAglyvpTCZp905jvXE9NP8hAc 2016-04-04 05:46:30 220.127.116.11 9001 0 m ghXqzv3gpKRCJ8LtQIe78XccMxf0/p2+/HmwC0LPaSo s Fast Running Stable Valid v Tor 0.2.4.27
As you can see, it contains the name, speed, version, flags, and IP address. So yes, you, me, the government, everyone has access to the list of nodes. This does not mean they can control the nodes, just that they know what their IP address is. As soon as a node is suspected compromised, a new version of the consensus is quickly released that blocks that node. Luckily, those events are rare and typically involve very mild issues (an evil exit node involved in petty password theft against people who are foolish enough to put their password into their bank without using the https version of the page).
Note that you are not a relay if you use the Tor network, you are just a client. The government does not have access to the list of people using Tor. You would have to intentionally configure Tor to become a relay for your IP to be listed on the public consensus, otherwise only volunteers who intentionally donate their bandwidth will be listed. So no, the list of Tor IPs does not help the government track people down.
To protect your anonymity, Tor is designed such as no one can monitor your activity. Your network traffic is directed to a Tor relay, which will direct it to a second one, which will finally direct it to a third one. They're just proxies designed to run the Tor network.
These three nodes are publicly known and listed by directory authorities. They must be public since clients need to know where to connect. The government has access to that list too.
Since we have the IP addresses, any government authority could contact their respective ISPs to learn who are running the Tor relays.