I mean non rechargeable alkaline batteries like energizer's, some full, some half empty. I know I cannot do that in series, I forgot why, but what about parallel?
I found answers for rechargeable batteries only.
The fresh batteries will attempt to 'charge' the older batteries, since there will be a voltage difference.
Depending on the type of battery, and the differences in voltage, the results may be anything from "It works just fine" to bulging and/or leaking and/or overheating batteries. The latter because these are not rechargeable.
With rechargeable batteries, the batteries with the higher voltages will charge the lower voltage batteries until they equalize.