All these are perfect ideas, but you might want to make sure that the people you save are going to be beneficial to the mountain survivors community that you would be making. You don't want to bring anyone that might destroy the safety of the group. People with aggressively arrogant or disturbing charismatic personalities are a no no to add to a group in a zombie situation. They will want to either take over or use others as cannon fodder to save thier on necks.
Also make sure to check as fully as possible that no one has been bitten. I would not bring any one that is not willing to show any areas that could have been bitten and covered up with clothing. They don't have to get naked, but they have to take have to be willing to take off the shirt and the pants. A person could easily bandage a bite wound and change clothes that have no blood on them. You would not know until it too late.
I can see pick them up if they are running from zombies and there is no time to check, but I would give them a quick look over to make sure there are no obvious bites. After we get clear of the zombies I would tell them if you want to continue traveling with me you to show me that you haven't been bitten anywhere. I would do the same.
These are the two main reasons people die needlessly in zombie movies.
