Learn Finnish: Hän joi suoraan tästä pullosta viiniä. - He drank directly from this bottle of wine.

This is the partitive attribute rule in action. When you have a phrase expressing a measure or container, the substance word (viiniä) stays in the partitive case even when the container word (pullo) inflects to match the rest of the sentence. So, pullo viiniä (a bottle of wine) becomes pullosta viiniä (from a bottle of wine).

Since Finnish word order is flexible, could viiniä just be the object of the verb joi?

Yes, structurally it could mean 'He drank wine directly from this bottle.' However, because viiniä sits right after tästä pullosta, native speakers will naturally read it as the cohesive phrase tästä pullosta viiniä ('from this bottle of wine'). To clearly separate them and say 'He drank wine from this bottle', you would usually change the word order to Hän joi viiniä suoraan tästä pullosta.

Could I just say tästä viinipullosta instead of tästä pullosta viiniä?

Yes, you can. Viinipullo (wine bottle) is a compound noun, so it would inflect entirely as tästä viinipullosta (from this wine bottle). The phrase tästä pullosta viiniä is slightly different because it emphasizes the quantity or contents, literally 'from this bottle-measure of wine'.

Why does 'directly' translate to suoraan instead of using the regular adverb ending -sti?