"We love them."
While the meaning is the same, 'Ich kochamy' puts a stronger emphasis on 'them', i.e. 'It is them, who we love'.
Whether or not it should be accepted is debatable.
As an answer to the question "who do you love?" "we love THEM" - it's fine. Otherwise should be "kochamy ich".
Both ich and je can mean "them" in the sense that it's used here. Ich means a male personal group (a group with at least one male person), and je means any other group.
"je kochamy" is wrong probably only for the same reason that "ich kochamy" is wrong (see above)
"kochamy je" should work though
bit too advanced for this stage, i will come back to it later and try to understand what you are saying ;)
Does anyone noticed: this lesson supposed to contain examples with nią i nich, but it actually didn't.
Is ich pronounced 'ivh'? I can see this getting confusing in learning multiple languages
If only you can do it another way, avoid putting a pronoun at the end of the sentence. It sounds really quite clumsy. For example here: "Kochamy ich" is a perfectly fine sentence (the alternative, putting 'ich' at the beginning would be really really bad), but "My kochamy ich" is clumsy, because you can easily say "My ich kochamy". Love is the most important information, not 'them'.
I still don't get it. In "Kochamy ich" the subject is implied. "My kochamy ich" would just have the subject explicitly included in the sentence, so why it would be wrong?
Yes, implied, but not explicitly put. As you use two words, the only two options are "Kochamy ich" or "Ich kochamy", and "Ich kochamy" is just too strange, you really shouldn't start with a personal pronoun in a different case than Nominative.
When you put this subject explicitly, the number of potential word orders grows. You can now not avoid putting 'ich' both at the beginning and at the end of the sentence, at the same time. Therefore you should do it :)