Perhaps. Although there's no evidence that teething causes fever, fevers of less than 100 degrees have been reported. If upper teeth trying to erupt vagus nerve stimulation can result in runny nose. As to appetite, would you want to eat if your teeth were sore? Please see Pediatric Dental Specialist (1st Dental exam Age 1). See Pediatrician to check for cold/virus. You must see both.
No. The symptoms you describe are associated with speeding up the eruption of the teeth, particularly a mild fever. So it is the fever causing the teething and not the other way around. A common myth.
Not likely, Seasonal flu is very common viral infection. Usually the condition resolves on its own with home care. Drink a lots of water and good rest. NO ASPIRIN! . If concerned, see your pediatrician.