The wiki's list of working titles should help out here.
Marvel Database also has a ton as a result of Doctor Who Magazine (and others).
I'd recommend this website for a history of the TARDIS prop. The sign has actually changed a lot over the years.
To answer those specific questions though: the original wording was actually "urgent calls" but this was eventually altered and "office" was a typo of "officers".
As the Class licence was acquired by Big Finish before it was cancelled both of the currently released volumes are set during the first series and do not reference the Weeping Angel cliffhanger. Hopefully that will change in the future though!
I wasn't satisfied with the "common theory" answer I provided so consulted the novelisation for some concrete proof and found it.
From the prologue:
Lydia Belmont's lottery numbers were "a combination of her house number and various birthdays, including Chris Rea's, the fourth of March." In the same paragraph we also learn that the upcoming Friday was Chris Rea's birthday. Wilson procrastinates giving her the ticket until "Friday night" at which point he is killed by the Autons.
Then in the first chapter, it is confirmed the day when Henrik's blew up was "simply a Friday" as Rose thought in the morning.
Glad to have this finally confirmed!
The wiki page for Roy Llewellyn gives 5 March as the date of the attack with AUDIO: One Rule as its sole source but I have not listened to it so don't know if the specific date is mentioned. Also 5 March is the day that Clara Oswald's mum died which is commonly theorised to be a result of the attack.
But the poster doesn't say she was last seen on the 6th, it says she's been missing since the 6th. Missing, in other words not there, in other words the day after she last saw Rose.
How do you work that out?
Rose is set from the 4th to the 5th. For Jackie, The End of the World takes place before the events of Rose. Note that in their phone conversation, Rose asks Jackie to put some money in the lottery syndicate that we saw her attempt to deliver to Wilson at the start of Rose.
The short story "Roses" is set just before the First Doctor is kidnapped and sent to the Death Zone. In televised terms, it is set between The Daleks' Master Plan and The Massacre. Steven is resting in the TARDIS during this period explaining his absence.
The example you gave regarding remembering multi-Doctor events is one of many contradictions. If you want to stick to a NuWho example, in Time Crash a major plot point is that the Tenth Doctor remembers the Fifth Doctor meeting him.
The Second Doctor can remember the War Games because of the idea of a Season 6B. Basically, just before he regenerated, the CIA (Celestial Intervention Agency) halted the process and turned him into their "hired gun" until they no longer needed him. It's an interesting topic, I advise you look into it further.
The Third Doctor is easily explained. It takes place for him during Season 11, as you say. He is just having a drive on his own when he is kidnapped. Additionally, I think his initial trust in Yates is just surprise that he and Liz are also in the Death Zone, not that he thinks of Yates as untrustworthy (his actions in IotD were a result of his conditioning by BOSS in The Green Death). Anyways, the Doctor quickly becomes suspicious of him.
I hope these answers are satisfactory to you.
The Feast of Steven
I don't know the actual reason but it was extremely offensive if you took the content seriously.
A Voord maybe?
Royal Blood comes first. Big Bang Generation comes next and Deep Time is last.