Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure.
1)Since weapons are useless in a melee, if I am about go to into one I don't want to lose my weapon. One choice is to hand it off to a fellow soldier before diving in, but if there are none around, can I just put id down on the ground by itself (i.e. leave it behind) and then come back and get it later?
No. Weapons can only be (a) handed off during a Move order at the cost of 1 MP or (b) voluntarily eliminated (and placed on the casualty track). CC has no mechanism for unpossessed weapons.
2)In scenario 3, special rule 4, my card G-65 is not sappers it is Demlotions. Is this a mistake? Not sure which card I should use, sappers or G-65.
"Sappers" is nothing but an evocative title for that particular special rule. It means nothing in game terms. The rule is correct as written.