When your Incapacitated health box is filled with damage (of any sort), you become Incapacitated. Any further damage past Incapacitated, whether from the same attack or a later one, sends you into torpor, unless it is aggravated, in which case you meet Final Death.
Bashing and lethal damage to a vampire in torpor typically don't do anything, although enough (decapitation, removal of the heart, etc) will still result in Final Death. Note that this is different from most other World of Darkness games in that there is no "wrap-around" where bashing damage converts to lethal and lethal to aggravated when damage off the chart is suffered. In fact, vampires don't even mark bashing and lethal separately, they just treat them both as "normal" damage and mark them both with the same slash.
Explosive and Incendiary ammunition is generally very exaggerated in fiction. Both usually have poor ballistics (ability to fly straight) and low penetration (ability to pierce armor/flesh/anything else). Also, the intention of using either is different from what you want to accomplish. Incendiary ammunition is usually paired with armor-piercing rounds to engage enemy aircraft - cause a leak in the fuel storage and then ignite it, and for that it starts flaming right after it leaves the barrel. Explosive ammunition is usually used against armored targets to blast away the armor a fraction of a second before the penetrator (a very hard core) of the bullet hits it. Contrary to the popular belief, none of those light up/detonate after the penetration.
What would happen to a vampire shot with this kind of ammunition?
A lot of damage, but not more than using a dedicated anti-personnel rounds. While incendiary will burn the vampire for a couple seconds if it stays in the wound, the explosive one is likely to just cause overpenetration - the bullet would make a hole in the enemy and fly right through him, without causing increased damage at all!
What kind of damage (bashing/lethal/aggravated) would she suffer?
For Explosive I would rule lethal. Incendiary - following the rule about flaming swords - aggravated, but that's just my opinion. Imagine a guy being shot with a gun and then having a firecracker sticked in the wound - that's the sort of situation we're looking at.
Can this ammunition be shot with a sniper rifle or a pistol ?
Most certainly, however you will have a problem finding such ammunition for a pistol - simply, these are designed for anti-materiel rifles and machineguns, not pistols.
How hard would it be to obtain?
Very hard, unless you have contacts in military. That ammunition is usually calssified as a destructive explosive device and unavailable to the public. Also, home production of this is very complicated and requires expert knowledge of chemistry, engineering, gunsmithing and uncommon tools and supplies.
Is this ammunition dangerous to use?
Yes, even more so if you're a vampire. While explosive rounds are simply a hazard, just like small grenades, incendiary rounds are known to damage the gun's barrel and make it prone for jamming. For drama, I would consider every botch a misfire that ends up with the rounds exploding dangerously close to PC's face.
I have found the ammunition in WoD combat, it says it causes great wounds, but they are only +1 damage, and type of damage is not specified. Are there any other source about the subject?
The duplicate question has better information about it.
Best Answer
Your example scenario:
Vamp starts full health (seven boxes):
Vamp takes 4 bashing.
V20 pg 285
So she only takes 2 Bashing and is now "Hurt". -1 dice penalty.
Vamp takes 3 lethal. This "pushes down" her bashing. The Vamp is now "Mauled", -2 dice penalty.
Vamp takes 2 Aggravated. She is now "Incapacitated" and can do nothing. Any further damage sends her into Torpor. Any Agg damage kills her.
V20 pg 283
Let's say the Vamp then took another level of Lethal, sending her into Torpor. We'd still mark the Lethal box above the Bashing, which would "push down" the Bashing damage. The damage in V20 doesn't roll back around, it falls off the track. Here's what she'd look like:
Applying Damage Penalties
V20 pg 282
So, as soon as you take damage of any kind that marks the "Crippled" box, you are at a -5 dice penalty to any action that would be affected by your injury. I usually read that as any action, since pain usually detracts from concentration as well as mobility. You can give vamps a little leeway with this, since they feel pain less acutely, but that's a Storyteller judgment call.