Respiratory problems can be common in guinea pigs, especially with guinea pigs that live in an enviroment that has a lot of dust. In order to minimize your guinea pig's risk of respiratory problems you should consider switching to a dust-free bedding instead of ceder or aspen type beddings which contain a lot of dust.
Yes, especially in poorly-treated ones from pet stores (in future, adopt). However, Upper Respiratory Infections are easily treatable (with doxycycline, bactrim or baytril, NOT amoxicillin) by specialized exotics vets.
Yes, especially if you get them from a pet store where they are abused and inbred (so please adopt). Some pigs are prone to illness, and you should always have respiratory issues seen by a trained EXOTICS vet - pigs go downhill fast if not treated.
Yes. You should take your guinea pig to an exotics vet (one who specialises in rodents, not an ordinary cat/dog vet) to get labs done in order to find out what is causing it. There are only a few safe antibiotics for guinea pigs so make sure your vet's qualified.
Yes, guinea pigs often get Upper Respiratory Infections especially if you bought them at a pet store (where they're inbred/missexed/treated horribly). Please take your pig to an EXOTICS vet for a checkup and get labs to see which of the safe meds (baytril, bactrim, doxycycline) will target the specific infection.