There's no rule stating "å elske" is to be used strictly for romantic relationships, but it's certainly an intense and rather intimate word when directed at a person.
By the time your daughter turns 10 she'll likely find it awkward if you say "Jeg elsker deg" to her in public, but you'd be hard pressed to find a parent that doesn't "elsker" their child.
Yes. If you say "mi jente" it sounds like you need to specify that it isn't someone elses girl you love. Unless someone says that you love "that girl over there", and you need to correct them or something like that, use jenta mi.
Also, you need to have much pressure on mi in mi jente. Say it the same pressurewise as in english. "I love MY girl" "Jeg elsker MI jente"
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No, all adjectives in front of the word. "Den røde bilen" = "The red car"
For where to place "min /mi" look at this http://folk.uio.no/helgelo/possproun.pdf it basically says that you can choose wether to put it in front of or after the word.
edit ninjas everywhere
double edit Of coure you would have to conjugate them differently depending on where you put "min"
When speaking about objects, placing the possessive first stresses the ownership more. It's often used if you feel the need to clarify that it's -your- something you're talking about.
Jeg elsker bilen min.
I love my car.
Det er MIN bil!
It's MY car!
However, that rule does not apply when speaking about people, as we do not own them. We can still stress the pronunciation of the possessive to make it abundantly clear that we're speaking of our mother as opposed to somebody else's, but the placement of the possessive doesn't stress this on its own like it does with objects.