So, here we go. (German is my major, so beware to ask these kind of questions

)
Dutch, as pointed out before, is the equivalent for our "Deutsch" which means "Germans" but is actually derived from Latin "theodiscus" which means "folklike" or "popular" and it was the word used for our language because educated people would speak Latin or French and the farmers and other uneducated people would speak German. It was therefore actually the term for "language of the people". Dutch and German were considered the same language for quite some time, and just as the Germans started to call themselves "Deutsch", the English picked up the word for the region of the "German"-speaking people closest to them - the Dutch. (German has a crazy variety of dialects, it's no surprise Dutch has developed in an own language.)
As for all the weird names for Germany:
We call it Deutschland (literally "land of the people").
All other names are derived from the variety of tribes that originally made up the "Germans" (So that's just an umbrella term). Most of the times, languages picked up the name of the tribe they had the most dealings with:
French/Spanish -> Allemagne/Alemania = Allemannen
Finnish -> Saksa = Sachsen (Related to the Anglo-Saxons)
Italian -> "tedesco" -> Actually the word we use (derived from "theodiscus" as well)
I hope that helped. =)