1. If you want to tell someone you're eating right now (so you're busy), yes "I'm eating" is perfect.
2. "I think" vs. "In my opinion" - "I think" has various uses, and one is the same as "In my opinion", but "In my opinion" is slightly more formal. You can also say "I believe..." "From my point of view..." "It seems to me...", etc. And, of course there is the extremely formal, only-for-writing "In the opinion of the author"
3. Thank you very much is good, or you can say things that show you understand how much effort or thought the person put into something. For example, if someone gives you a handmade gift "Wow, this must have taken a long time to make! Thank you very much!"