If vomiting and diarrhea go on for more than 2 days, or if there is fever, it is most likely a bacterial infection and antibiotics will be needed. Most food borne illness is viral, and should resolve within 1-3 days. Anything longer than that will require a dr visit. In short, prevent dehydration is the primary goal in the treatment, and stopping the vomiting.
Directly to your question - first, do not try to put anything in your child's mouth; that will only increase the chance that you obstruct the child's airway. Make sure that the child is laying somewhere where the seizure will not cause them to injure themselves, such as a concrete floor. Then, just keep the child protected from injury and watch for a short time, watch exactly what type of movements they are making so you can describe them well to the ER doctor. Nearly all of these seizures will stop within a minute or so. If it continues for much longer than a couple of minutes, I suggest you call 911, as it may be something else that paramedics can start to treat. If it stops after one minute or so and your child becomes alert again, place them in a comfortable place, and give them tylenol and ibuprofen to decrease the fever. Take their temperature so you can tell ER staff. Those are about the only things you need to do at first. Then you should go to the ER, as long as the child is alert, like I said. If they aren't, call 911.
In the ER, tests should be done to rule out causes of the fever, such as meningitis, ear infection, etc. It is not a "normal" side effect of the fever. Most children who get a feverdo not have a seizure. But some do, and it is due to the fever, although this is not really well understood. It is believed to be somewhat hereditary, in other words, many children who have a febrile seizure have a relative who also had these when they were young. Typically, as the child ages, the chances of a febrile seizure decrease. Also, the degree of fever does not seem to matter. A child with a temp of 101F can have the same seizure as one with a temp of 104F. The primary thing, when you first see that your child is having a seizure, is to protect them from harming themselves further by falling or hitting their head, etc. That is your first priority.
Cardiac disease can be very tricky, even for a Board Certified ER Dr., again, because not everyone has textbook symptoms. I have personally found 2 patients over my >20 year career who complained of a toothache, but something about them wasn't right. I asked them cardiac questions, we did an EKG, and they were both in the midst of having a heart attack. So I never let my guard down when it comes to this diagnosis. Hope that helps.