Hi, welcome to BYC!
It is my understanding that mites and other external parasites are MOSTLY species specific. Poultry lice live on birds. And poultry mites are different than dog mites. Poultry also have 3 different types of lice... feather, body, and head. And several types of mites as well.
While you might get a mite or a louse on you.. they will not stay on a human host. So no you won't become infested.
Salmonella or e-coli is a bigger concern IMO... but I am still learning something new every day.
As a kid, we did get scabies once after visiting the mountains... I think. I remember treating with a lotion. Memories are vague though.
Not inviting other wild birds is a good way to help combat parasites, as mentioned. But make sure you don't forget those nasty rats that'll be coming around for the feed shrapnel. They are major spreaders of parasites and disease, not to mention bird PREDATORS!
But also, if you do need to treat your birds... Permethrin spray is highly effective, affordable, easy and safe to use. There is an organic version made from pyrethrums, a chrysanthemum extract that the synthetic permethrin is based on if organic is important to you, sold under names like Spinosad or Elector PSP for many more $. IMHO, organic poison is STILL poison. So I go with the synthetic version (for now).
Please note that while many of us talk about nasty red mites or lice, the fact is there are a few types that are completely microscopic and you will NEVER see them even if they are crawling up your arm right now.
As far as I know you don't have to worry about catching round, hook, or whip worms. But I think people can catch tape worms and know they can get ring worm.
Hope your friend and their children enjoy their new birds!