ad 2) Yes, I can confirm that. The problem also occurs, if one uses a normal save. Happened to me the first time I went to enter the caves and saved before trying to get to the three lockers between the two security gates. Totally forgot to mention it because I avoided saving in such instances afterwards.
ad 4) If you have both tasks completed, you are supposed to check back with Hadrian Tanner (on the SGS commons level), though he doesn't have further missions for you. Basically, apart from the burrower caves behind the vault gate, you completed the demo.
Or do you mean the Notes also don't update anymore for other quests?