The stronger would prevail.
By your definition, no. There are good-aligned outsiders doing that (eladrins fighting a hopeless battle in the Abyss to protect a small community of eladrin children trapped there by Pale Night). For a god to go fighting other gods is generally referred to as suicide, and they do not like doing so in an open fashion. Generally, gods going off to do things themselves is bad juju.
Oh yes, quite a lot of them.2) Are there any deities residing on Baator?
Avernus
• Bargrivyek, goblin deity of cooperation
• Kurtulmak, chief deity of the kobolds
• Takhisis, Krynnish deity of evil
• Tiamat, draconic deity of chromatic dragons
Dis
• Druaga, Babylonian deity of fiend summoning
Minauros
• Hecate, Greek goddess of magic
Phlegethos
• Inanna, Sumerian deity of love and war
Stygia
• Kriesha, Cerilian deity of cold
• Sekolah, chief deity of the sahuagin
• Set, Egyptian deity of storms and the desert
Those are some of the more notable ones, but of course there are others. By and large, the gods do not establish realms below the fifth hell, though the Maztican deities set up a shared realm on Maladomini.
One petitioner that manifests as two bodies.3) I saw you discussed Dvati here. Do they make one or two petitioners upon death?
The Lady only communicates through the dabus. She is perfectly capable of understanding others, but that is how she expresses her will. In turn, as any direct exercise of her will tends to be... shall we say, immediate and horribly violent, asking her for something would still involve a dabus executing the actual request should she feel like honoring it.4) Have there been any cases of someone asking the Lady for something, not selfish, but for Sigil sake, and getting a reply? For example asking Her to protect everyone from something really horrid that could endanger the whole Sigil. I guess dabbuses can, but what of others?
So essentially, apart from the PCs asking for aid in Die Vecna Die, no, and even then there were dabus on hand to sort things out.
We do not get a great deal of information about the transitional experience, but essentially a petitioner is the person they were in life, only their conscious memories of life are a pleasant hazy background to their current state of existence - you can remind them of events, people, etc. and they will recognize what you are talking about and even respond fairly appropriately, but a petitioner does not spend their first moments feeling the pang of loss. Now, if they went to a Lower Plane, their first few moments (which might also be their last few moments) may certainly be spent experiencing negative emotions for all new reasons...5) How do people actually feel change from turning from a mortal to petitioner? Do they feel it at all? Is it something like "Goodbye, my loving great grandchildren, be good boys and girls... huh? Who am I? Where I am? Oh dear, what a beautiful mountain is over there!". Or the existing mind shuts down to a mathematical null, then a completely new entity appears?
See the response from Eldan. It is not a common thing, and most who have been mazed would have the sense not to return to Sigil if they ever got free. The Lady could maze someone twice, but generally if someone were to have been mazed, escaped the maze, and then decided the most clever thing to do was to return to her city and cross her a second time, I doubt she could be swayed to see any reason to let someone so transcendentally stupid continue to draw breath. Then again, you do never know what might amuse her.6) Except Duke Darkwood and Nameless One, have there been any successful escapes from Mazes? If there were, what happened to those people after that? Can\would a Lady maze someone twice?
None recorded in any meaningful detail. People tried. People died. It is not an interesting topic.7) Have there been cases of some clueless berks trying to harm the Lady with any kind of weapon? I know that all of them failed, but curious if there are some interesting stories about attempts.