Usually leaves that have lost their tips will remain "tipless". I found some brown tips on my aloe vera too, I pinched them off, and the leaves don't look too bad. If a majority of leaves have brown tips, it may be a disease, but otherwise leaves tend to get brown with age.

I'm not sure about rooting aloes from leaves . I've heard about propagating them using offsets and seeds, so my guess is "no".

Actually, Aloes can be put in full sun, or at least the brightest place possible. Give a soaking with water when the soil becomes dry. Don't let it become waterlogged unless you want more rot. Water less in winter than in summer. Give monthly fertilizer during spring and summer for best growth.

Well, good luck!

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~Lily