I would say that "kara amiko mia" is ok, but "kara mia amiko" is strange. For the second one, it would be better to say "mia kara amiko."
Not all speakers make this distinction, but for a large number of esperantists "mia planto" is definite (THE specific plant that I'm talking about) and "planto mia" is indefinite (a plant that belongs to me.)
Are mia and planto the wrong way round here?
Only sort of. I think someone tried to get cute. The vast majority of the time, the possessive pronoun (mia) will be first. There's a good argument that with pronouns like this, it actually changes the meaning (and not just the emphasis.)
Because the plant is doing the growing, rather than the thing being grown (by someone or something). If I was growing a plant, then it could be "Mi kresas planton mian" -- I am growing my plant. The subject (thing doing the verb) DOES NOT have the -n, and the object (thing the verb is done to) DOES have the -n.
No. That's pretty much what I was trying to say in my previous comment. Word order is pretty standard in Esperanto. Esperanto wasn't born yesterday. It has a 130 year unbroken history of regular usage, and all courses teach accordingly. The kind of variation you described is no more common among intermediate speakers of Esperanto than it is among intermediate speakers of, say, English.
I assume from your question that you had an English sentence to translate into Esperanto, unlike the sentence at the top of this page, which was Esperanto to be translated into English. If so, and the English had said "flowerpot", then "florpoto" would be accepted. But if the English says "pot", it should be translated "poto".