With pronouns, both orders are possible. With nouns, you can only say Jag älskar inte X. With pronouns, having the pronoun before inte is the normal order with standard meaning. Putting it after adds a shade of contradiction to the meaning. So Jag älskar dig inte is neutral, but Jag älskar inte dig may imply … 'but I love someone else'.
This is an old question but here's the answer for anyone else that might be wondering. There is a difference. Sometimes I find it helpful to listen to other speakers. Forvo.com is a good resource to train your ear to subtle differences.
well, technically no. Duolingo asks for literal translations (remember, it's a machine!) and here it specifically asks for the negative form "verb + inte". Also, meaningwise "to not love" is not the same as "to hate". I am sure not every person you don't love, you hate too ;)