1: aliens keep grenades on their belt (or elsewhere) until they decide to use them, at which point they throw them. they do not at any point physically put the grenade in the unit's hand, although they pay time units as though they did.
2: yes, enemies will make use of any weapons they have at their disposal, and make decisions based on their available options.
3: order doesn't matter, unless you give them multiple guns/melee weapons. the first two weapons (ie melee or firearms) will go in the hands, the rest will go wherever they fit. the AI doesn't assign them a priority based on their order, but rather their expected damage output and situational viability.
