Yes to both of your questions in the first sentance. If you have a user created file with custom stuff, you need to give it to the GM to avoid errors. Little hint? Every player should create a user file with their name, thus the GM knows who he has, and you never run into issues of guessing whos user file you have and did not rename. I also recommend custoim feats, traits etc. be held in a special user file named after the campaign, be updated by a player, and distributed to all players, thus you have a central repository for things all players may use. This way custom house creations are avilable exactly the same to all players in the campaign.
They can always load your character if missing books, but they will have some errors.
Your GM really needs to have every book the players do if he wants to load up and review everyone characters. It is just the way it is. If he trusts his players, and HeroLab, then he can just look at them quickly on everyones system to see if they have errors (assuming you all bring lappies or devices to game night).
Best part of HeroLab as a GM? I know that players characters are as accurate as possible, and I do not tend to review them. However I buy every source book, so if I do want too, I wont have issues.