I would like to know if Tor can cooperate with other applications, if the information leaks can be stopped and I can be anonymous. For instance on a messaging application, if someone were to try to get into my traffic and find out my location and see what I was saying, I want Tor to work on that application so that something like that doesn't happen. I want to know if this is possible, and if so, how can I set it up? Please help, thank you!
Your question is two fold. So :
1) "get into my traffic and find out my location" For this, you need tor. Install Orbot from f-droid.org client.
2) "see what I was saying" For this, you need something like OTR or any other end-to-end encrypted protocol like axolotl.
2.a) Install a chat client with OTR support. Install Chatsecure from f-droid.org client. Get a XMPP/Jabber account and set chatsecure to route traffic via tor. (it's very easy)
2.b) Install Textsecure from Playstore and route the app's traffik (or whole device's traffik) via tor using Orbot but this needs root access. Even if you don't use Tor with Textsecure, it is pretty secure already.
Both Linostar and user1552 have mentioned practical ways to help you to achieve what you are looking for. However, there is at least one addtional way that your location maybe computed. That method is called triangulation. https://en.wikipedia.org/wiki/Triangulation
What basically triangulation refer to in the sense of figuring out your location while you are using or carrying a cellphone is the point that your cell phone send/receive signal to/from the several BTS(base transceiver station), The magnitude and strenght of these signals indicate the distance to each BTS. By measuring the signal level from your cellphone to at least three of these BTSes, one can compute your location using triangulation method. This maybe possible to do even if your cellphone is off. The only ways to disable your cellphone so that it does not report your location is either to leave it at home and powered on, or take it with you but take the batteries out of the cellphone. From these two methods, leaving the cellphone at home and powered on, is preferable. In this method nobody get suspicious why your cellphone is off. For more information regarding A base transceiver station (BTS) look at this link: https://en.wikipedia.org/wiki/Base_transceiver_station
Yes, Tor can be combined with additional applications (like PGP email encryption software), protocols (like SSL/TLS), or networks (like VPN) to further increase your security and protect your anonymity.
As for using Tor on your mobile device, if it is an Android, you can use ORWeb in conjuction with ORBot. For Apple iOS devices, you can use Onion Browser. You can even setup your computer as a Tor proxy and access point, and let your mobile devices connect to Tor through your computer, without need to install any mobile apps.