Does a Mitsubishi Triton have a timing belt?

My mechanic is trying to charge me $3,000 for a transmission replacement for my 2007 Lexus ES 350. That seems pretty steep to me. I that a normal price for a job like that?

Someone told me that Chryslers use the same engines as Mercedes, but there’s no way that’s true. I’ve driven a 2015 300C before and it’s nice, but it’s no Mercedes. What type of engines does Chrysler use in the 300C?

My credit score is over 700 and this is my first car loan ever. I feel like it's a good deal, but I would like a second opinion.