Borderlands – Why is the pistol a grenade

I can't provide exact numbers, but I have noticed that the more ammo left in the clip, the bigger the boom and the higher the damage. So firing once and then throwing your gun will cause quite a bit more damage than throwing an empty gun.

The usefulness of this is balanced by the fact that any ammo in your clip is used up when you throw the weapon. So an almost-full clip will do more damage but it chews through your ammo in no time at all - and of course you have to actually hit your target for it to be of any worth.

Note that you can't throw your 'last' weapon - i.e. if you don't have enough ammo to do a proper reload, your character won't throw the weapon.

Edit - More info based on Ben Brocka's comments: The explosions appear to always be the same size but the damage is affected by the gun's Damage stat. It's a fair assumption that Gun Damage would be the relevant Badass skill, then. Experimental evidence with Badass ranks enabled/disabled would be useful to confirm this.

Additionally, if you throw an elemental weapon, the explosion will do damage of that elemental type (e.g. throwing a Corrosive weapon will produce a Corrosive explosion). Non-elemental weapons and explosive weapons both deal explosive damage.

Yes and no. As I eluded to in the comments, this takes effect only with "electrocute" Damage Over Time effects. Whether or not they're a result of your skills or guns doesn't matter, it just has to be electric DOT caused by you (deathtrap counts as you).

How it really works is every time an enemy takes electrocute Damage Over Time, there's a chance they'll catch fire, too. It never seems to start upon the initial hit with a Shock attack, and it can happen if you stop shooting but let the enemy fry for a second. Most of Gaige's electrical skills will induce Damage Over Time, so many of them have a chance to burn as well.