What's the difference between the meaning of 愛 ai and 恋 koi?
Is it like Ai means Love towards a friend or relative, and Koi is Love towards your boyfriend/girlfriend, spouse, etc?

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You can see my answer on
http://www.italki.com/question/298150

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Koi is pretty much what you described - romantic feelings and love.
Ai is much more broad.  
It includes koi and all the other kinds of love - it is "love" in its most general sense.

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My Japanese friends said that ai is the kind of love Jesus has for us -   unconditional. Koi being romantic in nature.

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Koi means fall in love, love is more deeply than koi.
It means affection, with no reward.
I hope this helps you.