Guppies will just hang quietly when they are scared. Not run away or get eaten scared but tentative scared. They don't know what to do and are just sitting waiting to see.
Chances are in a day or two they will settle down, do some exploring and start to eat.
A lot of it comes down to personality.
I have a couple females I can't put in a tank by themselves to drop, they just get so scared, but if I put one or two of my young half blacks in every is just fine, I use them because they don't eat fry.
I wouldn't breed the nervous ones if I didn't have to. A lot of that behavior just comes down to genetics.
But in any case, it's pretty common for them to just hang and scope things out for a day or two when coming to a new home.
As far as diseases, yep guppies can get all of the common ones. I don't know that they are a lot worse than other fish. Sometimes I think the mass raising and transportation and such that is common with them cause the guppies at the fish stores to have more problems when you buy them than some other fish.
I think they probably have fewer problems with parasites than some other fish. But most people never treat or are aware of parasites since usually they don't cause obvious symptoms. Jungle makes a great parasite treatment (parasite clear) that it's worth it to just routinely treat new fish during their month or so of quarantine and get rid of the gill flukes and worms and such.
Marv