A: When Rachel first arrived in the mainstream timeline it was believed her mother was actually the Phoenix Force. One that hadn't commited suicide on the moon, but had instead been lobotomized by the Shi'ar instead. It was sort of confirmed in the last response in the letters page of Excalibur #13. But then in Excalibur #52 the Phoenix Force revealed Rachel's true background. In her timeline the X-Men had never encountered the Phoenix and that the Phoenix had given Rachel false memories.
Q: Which one is her father? Scott or Logan?
A: Early on there was a question if Cyclops was really Rachel's father. Most of this stems from UXM Annual #14. In it Cyclops and the Invisible Woman are turned into Hounds by Ahab to track down their children. Susan is able to locate both versions of her son, while Scott couldn't find Rachel (I have my own theory on why Scott couldn't locate her, but it would be too long to post. Email me if you want to know it.)
But in later issues more evidence was shown that Cyclops is indeed Rachel's father. Most notably in Excalibur #74. In it Mr. Sinister gets his hands on a sample of Rachel's DNA and examines it. What he finds out is that she is indeed a Summers, but one whose genetic path diverged at some point. That makes sense considering that Rachel is from an alternative timeline.
Q: Just how old was she at her arrival in the mainstream timeline?
A: When Rachel first appeared in DoFPast, she appeared to be in her early to mid thirties. When she made her way back to the past she was about seventeen or eighteen.
Q: Just how close was she to Franklin Richards?
A: Extremely close. It would be best to check out Franklin's entry on the loves section of this site.
Q: What were the marks on her face all about?
A: They are tattoos called 'Hound Scars' which were branded onto the face to identify a mutant as a Hound.
Q: What happened to her after she was taken by Spiral to Mojoverse?
A: Not much is known. All we know is that Mojo used Rachel is his movies. A trade paperback was promised about her time in the Mojoverse, but was never followed through.
Q: Why on earth did Rachel use a red version of her Hound outfit as her working costume?
A: Most likely as a reminder of her past and a representation of what she is trying to prevent from happening in the future.
Q: Why was another Rachel never scene during the Cross-Time Capers?
A: For me it's rather simple. Since there is one (supposedly) Phoenix Force that can exist at one time in the multiverse, our Rachel was the only one that was sent back in time. That's what made her unique. All the other Rachels were stuck in their timelines. And in the timelines they visited during their travels, they usually arrived at a time period roughly near the time that they left. It's possible that it's version of Rachel hadn't been born yet, was still a child, or in America. Remember, Excalibur usually ended up in Britain. Not always, but most of the time.
Q: Why did she always dress so scantily?
A: That question can most likely be answered in two parts. The first is that's an influence of the Phoenix Force. It is the embodiment of passion and life, and its avatar would reflect it. The second is that Rachel was de-humanized for a good portion of her life. And once she had the chance, Rachel decided to express herself.
Q: When Rachel returned after being reborn, why did she stop manifesting the hound scars and outfit?
A: Because for once she knew who she was and was in control of her life. All her memories were returned to her and the false was recognized as such. Nothing was manipulating her anymore, and she could go on with her life.
Q: What exactly is the connection between Cable and Rachel?
A: Besides the fact that they're brother and sister? When Nathan was still a baby Rachel formed a strong mental link between them. As Mother Askani and after death, Rachel watched over her brother and guided him.
Q: Where did she go off to when she traded places with Captain Britain?
A: Rachel took Brian's place in the timestream and stayed there until she (decided to) emerged two thousand years in the future.
Q: What's the deal with the Askani?
A: Two thousand years in the future Rachel found a world ruled by the heavy hand of Apocalypse. Determined to end his reign she gathered those about her and formed the Askani, a group that looked forward to when the Chosen One would arrive. See the askani section for more info.