Okay, it's time for the answers .
Before I give them, it must be stated that the basic question concerned the original "Jet Set Willy II", and the bonus question concerned the revision of "Jet Set Willy II+" hosted (since November 2016 and still at the time of this message being written on 11th March 2017) on Julian D. A. Wiseman's website, which is, in fact, "Version +e.2" (as stated in the scrolling message on the title screen). It has since transpired that newer revisions of "JSWII+" have been created and "the last update" is "Version +e.22" hosted on this forum.
So the correct answer to both questions is A . Both the original "JSWII" and "JSWII+" Ver. +e.2 can be completed (in the sense of reaching "Oh $#!+!The Central Cavern!" after the toilet run) in less than 45 minutes of in-game time .
I have been able to complete the original "JSWII", with the minimum necessary number of 150 items collected and some lives lost in order to gain time, at 00:42:42. Additionally (beyond the quiz question), I have been able to complete the game with all 175 items collected and no loss of life at 01:08:11 in-game time.The RZX recordings of both of these walkthroughs have now been added to the original recording of "JSWII" done by AndyC and hosted on RZX Archive since August 2004, and can be downloaded from here.
As far as "JSWII+" Ver. +e.2 is concerned, I have been able to complete it, with the minimum necessary number of 180 items collected and some lives lost in order to gain time, at 00:44:42 in-game time. I really had to push this one to the limit to go below 45 minutes, re-recording the walkthrough for efficiency and looking for a more optimal route. Completing this version with all 207 items collected and no loss of life has taken me, in turn, 01:12:56 of in-game time. The RZX recordings of both of these walkthroughs have now been included (as a historical curiosity) in an updated set of recordings of "JSWII+" hosted on RZX Archive and can be downloaded from here.
Now, as far as "the last update" of "JSWII+" is concerned, i.e. "Version +e.22", I have been been able to complete it, with the minimum necessary number of 298 items collected and some lives lost in order to gain time, at 00:52:59 (to be precise, I collected 299 items, because the bathroom tap was collected inadvertently during the toilet run), and with all 325 items collected and two lives lost (which is necessary to collect some of the items) at 01:16:30 in-game time. The RZX recordings of both of these walkthroughs are in the ZIP file which was mentioned above, hosted on RZX Archive, which can be downloaded from here.
All of these completion times are only possible thanks to an extensive use of the Rollback feature in ZX Spin, which is the ultimate game changer (pun intended) .