It can be plural (think you addressing your children); also I think in "old" French saying to someone that you love them in the formal is correct, for example if you're courting a woman; you wouldn't address her in the familiar until she accepts you. At least that was the case in "old" Spanish.
(my guess) it's just the way french grammar is. later on you learn other phrases like je l'aime = i like it... i guess you're more or less asking why don't we say "i you love" in english? that's just not grammatically correct. in this case, we can't translate these words directly from english to french, because that's just not how the language works. it kind of reminds me of japanese language who always puts the verb at the end of the sentence.
If you say "Je vous aime" to your children, it's just as personal. I think "Je vous aime" adressing a single person in a formal way is not common anymore, it sounds rather medieval :)
I think adoring someone is a little different. It's both a sign of affection but if someone (you don't love) did something really awesome for you, you might say that he's awesome and you adore him for what he has done. I learned that "adorer" can also be translated with to apotheosize, to idolize or to lionize.
"je t'adore" can be a kind of joke: someone saying something funny or weird can be responded that without any sense of adoration (like gods or icons, etc).
"j'adore le chocolat" is also very common.
To make a long story short, expressing one's feelings or sentiments with "like, love, adore, worship", "aimer (un peu, beaucoup, à la folie, énormément, bien...), adorer, vénérer, révérer,..." is up to the speaker's choice and the object of his/her love/amour.
aimer is used to mean 'love' when applies to people, but 'like' when applied to things/non-animate objects etc. So people aimer=to love, otherwise it is like. You must have missed that bit. If you want to use aimer to mean 'like' with people you put bien after it. J'aime Jaques - I love Jaques. J'aime bien Jaques - I like Jaques.
not the most famous. as integra1 pointed out Je t'aime is the most famous but it still doesn't explain why it would be wrong to say Je t'adore. they use adore to say they love a piece of clothing or to say they love doing something but still why can't you say Je t'adore or why is it marked wrong.