It seems to me that the most languages have either complicated morphology or very strict word order. Are there languages with simple morphology and free word order (for instance, indicating relationships of words mostly with prepositions)?
Chinook Jargon is such a language. It is a pidgin with elements from English, French, Athabaskan and other Native American languages. But the morphology is isolating, like Chinese. The word order may be SOV with prepositions, just like English, or it may be head final like other languages, depending on speaker's preference and background.
Yes, there are. Head-marking languages generally allow for free word order in case the language is caseless. Macedonian pops to mind, a language without cases on nouns but with free word order. Grammatical relations are indicated by clitics attached to the verb. Likewise, Northwest Caucasian languages have free word order and little morphology. In Circassian, only specific NPs are marked for case; Abkhaz lacks cases altogether.