Sorry about the length, hope this helps.
1. The Joker is also very skilled in the field of chemistry (The Joker is also skilled in genetics and computer technology and proven to be a mad genius, and is no slouch at hand-to-hand combat. It is often implied that the Joker was transformed both physically and mentally by the accident in the chemical plant.(wikipedia)
2. The dangerous experiments placed a deliberate overdose of plant and animal based toxins into her blood stream that make her touch deadly and allowed her to boost her immunity to all poisons, viruses, bacteria, and fungi. Some comics have even gone so far as to depict her as more plant than human, breathing CO2 and requiring sunlight to survive.
Ivy is known to be able to seduce men and women alike, often using pheromones to do so. This (and her relationship with Harley Quinn) have led some fans to believe that she is bisexual, although most stories make it clear that Ivy is uninterested in any sort of romantic relationship with humans.
She specializes in hybrids and can create the most potently powerful toxins in Gotham City. Often these are secreted from her lips and administered via a kiss. They come in a number of varieties, from mind controlling drugs to instantly fatal necrotics. Her skin is toxic as well, although contact with it is usually not fatal.
In some adaptations she can control plants via telepathy. For example, in Arkham Asylum: Living Hell she was able to manipulate plants telepathically, using roots to form supports for a tunnel she and another inmate named Magpie were digging to escape, and also spawning glowing fungi to entertain Magpie.
Appearing in Gotham the same year as Batman, her aforementioned control of plants has increased significantly with each passing year. Before, just being able to manipulate plants such as vines ( Batman: The Long Halloween for example), she has since become stronger. In Greg Rucka's Fruit of the Earth storyline, she controlled an entire tree to come down on Clayface, ensnaring him in its branches. More recently, in Batman & Poison Ivy: Cast Shadows, she can be seen bringing down a whole skyscraper with giant vines. Her increased strength has only recently been brought to everyone's attention in Face the Face.
She has been known to carry a cross-bow and a vine whip which she also has used as a lasso. At times, the vine has had thorns on it. She also occasionally uses hand thrown and blowpipe launched poisoned darts.
Poison Ivy's athletic abilities have grown over the course of her career. She has learned a limited style of martial arts fighting. She is a proficient at climbing and leaping. She is a strong and fast swimmer.(Wikipedia
3. Yes, if Batman actullay refers to people as "friends", he was an ally. Batman believed that he, Gordon and Dent would be the ones to change Gotham. Harvey's accident only led to Gotham becoming worse and the rise of the "freaks". Batman The Long Halloween, is a good source for this story. Also, Harvey is White.
4. A revision in Catwoman's origin, and the introduction of the modern version of the character, came in 1986 when writer Frank Miller and artist David Mazzucchelli published Batman: Year One, a revision of Batmans origin. In the course of the story, the origin of Catwoman was also re-envisioned. A 5'7" Selina Kyle was reintroduced as a cat-loving prostitute/dominatrix who was inspired to become a costumed cat burglar when she saw Batman in action.
Miller's Year One origin was expanded on in the 1989 Catwoman limited series (collected in trade paperback form as Catwoman: Her Sister's Keeper) by writer Mindy Newell and artist J.J. Birch. This series explored Catwomans early career, a period that was tinged with tragedy as her former pimp Stan abducted her sister Maggie and violently abused her. Selina killed Stan to save her sister, and was able to do so with impunity.
Batman: Dark Victory, the sequel to The Long Halloween, implied that Catwoman suspected she was the long-lost illegitimate daughter of Carmine Falcone, although she found no definitive proof of this. Selina's connection to the Falcone family was further explored in the recent miniseries Catwoman: When in Rome (September 2004-June 2005). Though more circumstantial evidence was added to the theory of Selina's Falcone heritage, no definitive proof was provided.
It is currently unclear what portions of these stories remain canonical to Catwomans current origin, as various stories (and editors) over the years have posited that Selina was never a prostitute, and that other events depicted in those stories never happened. Zero Hour was used to retcon her history as a prostitute; in the Catwoman: Year One story (Catwoman Annual #2, 1998), Selina accepted an offer to "lay low" by posing as a prostitute following a disastrous burglary, and adopted the guise of a dominatrix in order to trick men into giving up information for use in future crimes. According to this revision, she also became a student of the Armless Master of Gotham, receiving education in martial arts and culture. This version of her story was tailored to fit in with her appearance in Batman: Year One while rendering the 1989 Catwoman limited series noncanonical. Batman editor Dennis O'Neil later stated that in the post-Zero Hour continuity, Catwoman had never been a prostitute. However, characters introduced in those stories (such as Selinas young friend Holly from Batman: Year One, and her sister Maggie from the 1989 miniseries) continue to appear regularly in the Catwoman series, and aspects of those plots are occasionally referenced, including recent issues that show Holly recalling her days as a prostitute with Catwoman. (Wikipedia)
I doubt Catwoman would sell Batman out, she's reformed and is considered part of the "bat-family"
5. Stirk has the apparent ability to cause fear or hallucinations in others with telepathy. Stirk was released from Arkham Asylum, where he was confined at the age of 16 for trying to kill a classmate, after being certified as sane probably following his use of his psychic abilities on his doctors. He then subsequently stopped taking his medication of tricyclics and chloropromazine and began his escalation into a serial killer.
A sociopath who takes sadistic pleasure in the pain of others, Stirk, like Scarecrow, uses fear to get to his victims. Stirk has the ability to make other people see him as someone else, allowing him to get close to his victims. He operates under the delusion that he requires the nutrients and hormones from peoples' hearts in order to stay alive, and these are best prepared with norepinephrine by inducing fear in the victim prior to death. (Wikipedia)
6. I don't think the fear gas is lethal in a poison sense, but usually it causes the person to hallucinate and go crazy and they sometimes end up dying of a heart attack, killing themselves or going into a panic induced coma. There is no antidote, or at least not that I know of.
