If i bought duracell AA batteries from target or wal mart, how many times longer do you think they will last compared to panasonic AA batteries from a 99 cents store?
what if the panasonics were not alkaline?

Michael P gave a good answer. Panasonic alkalines are about as good as Duracell. But at a 99¢ store, you may actually be buying carbon-zinc batteries which will last only two-thirds to one-third, as long. Those are distinguishable because they do NOT say Alkaline on them, but instead say Industrial or Heavy Duty.

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I have many alkaline batteries needing to be correctly disposed of, but I don't know how to correctly dispose of them.

Directly from the Duracell web site:
Alkaline batteries can be safely disposed of with normal household waste. Due to concerns about mercury in the municipal solid waste stream, Duracell has voluntarily eliminated all of the added mercury from its alkaline batteries since 1993 — while maintaining the performance you demand. Our alkaline batteries are composed primarily of common metals — steel, zinc and manganese — and do not pose a health or environmental risk during normal use or disposal. Read the rest of this entry