#1.
Roj Blake and Arnold Rimmer are cousins.
Well, s'obvious, isn't it? Look at Blake's uncle. Look at Rimmer's father. They're the exact same person. Fairly different in character, obviously, but I explain that thusly: Ushton = big bad criminal, yes? Which was why he was sent to Exbar. Rimmer Sn. = we only know him through Rimmer's view of him, but he seemed to be freakishly obsessive about law and order generally. Or at least obsessive, even if not actually freakishly so. He desperatly wanted to join the military, and passed on to his son a huge fear of authority. Obviously that was all a cover, and after his subversive doings were discovered and he was sentenced to exile he was forced to give up all his posturing and deal with the reality of being stranded on a cold, primitive planet (which is so cold as to require environmental suits, yet somehow Inga doesn't seem affected while running around in a pseudo-Indian costume... But we'll leave Inga alone. Which is the best thing to do with her really). The man we saw in Hostage was the result of fighting for survival with very little human contact.
And then there's the issue of names. I think the Blake clan changed their name from Rimmer at some point. Maybe Blake Sn. wanted to distance himself from his brother's (Ushton's) crimes, possibly in the hope of discouraging the Powers That Be from including his family in the punishment of his brother. Or perhaps one of them just happened to be a fan of ancient poetry and thought that 'Rimmer' sounded like a lavatory disinfectant.
Thankfully Red Dwarf doesn't have an actual dateline and neither does Blake's 7, so there's no problem there. However, what sociological background we do know seems to differ quite significantly. Of course, B7 did concern itself only (where the solar system is concerned) with Earth, described as the 'heart of the Federation's power'. Red Dwarf, on the other hand, dealt with Earth only as an abstract concept - Lister's ultimate goal. Rimmer was born and educated on Io, Lister lived on Mimas for the few years prior to joining the Jupiter Mining Corporation (This in itself seems to demonstrate a level of geographical mobility that is absent in the Blake's 7 universe, but considering Lister doesn't have the slightest clue how he got there it's very possible that illegal transports are running. After all, we know smuggling's still reasonably profitable). Anyway, back to the point... While B7 deals with Earth as an actuality - Blake, Jenna, Avon, Vila and Gan were all tried and convicted on Earth, so presumably that was their planet of residence, they talk about it constantly, they went there and blew bits of it up; Red Dwarf deals with a romanticized concept of Earth - Lister's romanticized concept, to be precise - of which Rimmer is very disparaging. I choose to believe that this attitude comes about from, not personal experience, but experience of his family members. My theory is that Rimmer Sn./Ushton moved to Io through legal channels fairly early on in his life, but his brother stayed behind on Earth. Possibly he (Rimmer Sn./Ushton) saw Io as a place with less state control than Earth, but either way his son has ended up not very keen about his planet of origin, suggesting that he has been taught it is not a pleasant place to live.
And then there's Inga. In order to explain her, I choose to believe that Ushton's crime, or at least one of them, was carrying on with another lady. The upshot of which was Inga. And he probably upset a few more people along the way, like he was shagging the wife of someone important, and she killed herself when he wouldn't leave his wife ("an old trout" Kryten) for her. So, it's not a very good explanation, but then Inga's a big wet pile of nothing and doesn't deserve a decent explanation anyway.
So, with all this coming out of the woodwork, the old trout decided she'd had enough and turned him in, in return for which, her and her sons were granted immunity. She pretended he was dead (hence the "your father is dad" letter) to avoid all the usual ramifications of being related to a Bad Person, which was why Arnie never found out he had a sister.
Although I still don't know why the exiled Ushton (which, for simplicity's sake, I'm assuming is his first name) was on such good terms with the Blake clan, but then I don't know why young Roj would have been visiting his uncle on a penal planet in the first place...
One possible identity for Blake Sn. is Rimmer's (Arnold Rimmer's, I mean) Uncle Frank. The one who was shagging his mum. The only problem with that theory is Rimmer's Uncle Frank had twin girls. ("Now, I know Sarah fancied me, but I wasn't too sure about Alice...") and Roj only mentioned having one sister. Of course, it's possible that a) one of them got a sex change, b) Roj's other sister still lived on Earth and just didn't get a mention, c) their dads had another brother, or d) Uncle Frank was just a family friend and nothing to do with this tangled web of deceit.
See? All makes sense.
This was all originally working up to a hilarious B7/Red Dwarf crossover, but then I realised it was a bit too contrived and it wouldn't be that funny anyway...
#2.
Ensor was one of the original members of Dave Dee, Dozy, Beaky, Mick and Tich.
Listen to Zabadak! They say Orac. The backing guys do, I mean. I'm nominating Ensor for Tich.
I bet they got Orac to play synthesizer.
#3.
The REAL reason the show ended.
S'Servie's hair, innit? Look at her in the first series. Not a lot of hair, I'll agree (in fact, she still has less than Travis, and he's supposed to be a big tough military man), but then compare it to the haircut from series four, where you can see her scalp quite clearly if the light's right. If they'd have been brought back for another series, she would have had to shave her head, and then maybe even Avon would have had second thoughts about snogging her...
or...