Is it safe to stop the Tor browser and network, and start using something like internet explorer or google chrome after? Like If I accidentally saw cp and deleted Tor and then started using my normal internet and browsers am I at risk for being caught or getting in trouble etc.? If me and my brother use a laptop each (as in 2 total) and I have Tor and am buying drugs, and he is not and is watching youtube or searching google , am I at risk? LASTLY something particularly worrying happened, after browsing with Tor for a day, I stopped, deleted it, and went back to google chrome and my un hidden use of internet, I went to youtube and noticed all the recommended videos and channels, they were specifically from genres or themes of the sites I had visited, like completely japanese channels and videos, about guns, and various things I had searched about while using Tor... *note I never used google,fb, gov sites or anything like that. So is this a sign I compromised myself somehow leaking my IP address? The recommendations were from only what I did on Tor. Am just lucky not to have been spotted by authorities?
Before I get into the meat of the answers, let me just advise you to stay away from the sketchy side of the web if you are not very knowledgeable about security. I've been using TOR for several years now and I've yet to see a single piece of CP so my only conclusion is that you probably need to reevaluate your browsing habits if you accidentally stumbled upon it.
Alright, to your questions now...
Q: Is it safe to use regular browsers like Chrome or Firefox after using Tor?
A: Yes. You can safely use other browsers, while, after or before using Tor. This applies to any software really unless its intentionally designed to collect data on or tamper with TBB.
Q: If I accidentally saw something illegal am I at risk of getting in trouble?
A: Its important to separate the technical part of this question from the legal part of this question. Technically speaking Tor offers anonymity by funneling traffic through a series of relays. While it is possible for an adversary to deanonymize users, its very unlikely given the circumstances you stated, that an adversary (namely law enforcement) would have known what you were doing, other than connecting to the Tor network (which is not a crime per se).
Now for the legal part. I'm going to assume you live in the United States--but if you don't ignore this. If you accidentally stumbled upon illegal material as you say, you shouldn't have to worry at all (and no, deleting Tor doesn't help, it just makes you look guilty). Law enforcement has to collect information that proves beyond reasonable doubt that you not only viewed this material, but did so intentionally (which requires mulitple instances of this to occur). No reasonable court would convict someone for allegedly viewing an image once.
Q: If I'm using Tor while someone else is using my network, can this affect my security?
A: No. While it is possible for another user on your network to potentially monitor your traffic, meaning they can know its headed for an entry node but they wouldn't know its contents. Also, they shouldn't be able to tamper with it at this point either as it is encrypted.
Q: Is it possible that I leaked identifying information while using Tor such that services like Google now associate my previous Tor session with me?
A: Did you log into an account you use for clearnet over Tor? Did you accidentally use Firefox instead of TBB? The most likely scenario is that your brothers activity is showing up.
In closing let me say that I am by no means an expert so if anyone wants to correct me, by all means do. Also, there are probably a lot of spelling and grammar mistakes so pardon that as well.