Hi Adam,
In answer to question 1, it won’t retrospectively discount the initial journey, but it will lower the off-peak cap for that day which the initial journey will count towards as long as it started after 0930.
As for question 2, it depends. As far as I know railcards do not actually have a start date. I also don’t know how quickly they’ll send out the railcard. If it’s a 1-year railcard then I’d get the discount added when you first travel to somewhere that can do it. If it’s a 3-year railcard there is another annoying consideration. The TfL system will allow the expiry date to be exactly 3 years from the date the discount is added, but railcards issued by post have an extra 5 days added to account for a slow postal delivery. If you take the railcard to be added on the day you receive it the system won’t allow them to put in the real expiry date. What they usually do is record the expiry as two years hence, then you have to get that updated at some point after the extra days have finished.