"I definitely do not trust the police."
Translation:Jag litar definitivt inte på polisen.
Those are very good questions. It boils down to what you want to modify. In this case, definitivt is modifying inte, so it comes först. In a sentence such as "Jag tittar inte mycket på tv" ("I don't watch much tv"), inte is modifying mycket, and hence the adverb order is the other way around. If you have multiple adverbs modifying the same word, you would usually separate them by commas, e.g. "Jag älskar dig oerhört, väldigt, vansinnigt mycket!"
For your second question (the reply got so long): there are two word orders you can use, although they are not always equivalent. The basic one is the one in this example, and you would be correct - all of the adverbs here should go between the verb and the particle. For sentences that begin with an adverb, however, subject and verb switch order with each other. Case 1: "Jag tittar inte mycket på tv", vs case 2: "Vanligtvis tittar jag inte mycket på tv". The adverbs that are not used to signalise start-of-phrase are still in the same place, in the same order. Hope that helped! :)