Q:Will freshly-charged rechargeable batteries lose that charge if those batteries sit unused in a drawer for two or three months?

1.Yes - different chemistries are worse than others for self-discharge. Poor performers include nickel chemistries, but watch out - nickel cadmium batteries can also exhibit a 'memory' effect, whereby if they are only lightly discharged before recharging, they will only appear to hold the relatively small top-up charge. For this reason nickel batteries should be fully discharged before recharging. Although lithium rechargeables show self-discharge, it is quite low and they do not exhibit the memory effect of NiCd.

2.More than likely yes , I keep my batteries in the freezer , even normal batteries can be put in a baggie and they will work again , after a hour or so - The ones that have gone dead -- Country Learning - lol

3.yes freshely-charged rechargeble batteries lose that charge if those batteries sit unused in a drawer for two or three months because charge leak through the air.

4.err, no - no more than electricity drips out of a light fitting if the bulb is removed! Air is an insulator. Batteries self-discharge through internal current leakage, made worse by high temperatures and damage to the separator.