Just like we say 'manga' to refer to Japanese comics, but the word 'manga' just means 'comics', and is used for comics from any part of the world in Japanese. Again, while 'manga' has been taken into the English language to refer to specifically Japanese comics, manga is still a subset of comics, and 'comic' still applies, except to kids yelling "Mooom! They're not comics! They're MANGA! And these other ones are GRAPHIC NOVELS! I'm an adult!"
Anime is just as much Cartoon as Family Guy, The Simpsons, and King of the Hill


Doumo is like 'very' or 'much' or whatever. It's often used to imply the 'thanks' part by itself. It's almost set to the whole 'thank you' expression, but you do see it in other places every now and then.