You should be able to. Save at the end of week 1, when the game tells you so. If you experience any bug, report it (not here).
There is none yet. All Jessie's content is going to be included into Week 2 - Extended Edition.
Vinovella will release it once week 2 is completed (which is not going to happen before summer).
Actually, when you will play Week 2 - Extended Edition, you could still access Jessie's scenes even without having played week 1. You should just start a new game and select Jessie among your love interests. Currently, her profile is hidden (in the Extended Edition it is going to be displayed together with Stacy, Polly/Nora, Vanessa and Chloe).