Yes possible. But first see your doctor to rule out other serious problems for dizziness before you visit allergy specialist.
Yes. Allergies can cause people to feel light-headed and dizzy. A severe allergic reaction could cause someone to pass out. See an allergist for evaluation. People with severe allergic reactions especially to foods or bee stings often need to carry emergency medicine like epipen (epinephrine).
Not typically. Allergies can cause significant congestion, and sometimes if that congestion occurs within the ear, sufferers may feel slightly dizzy. But allergies should not cause fevers, and the two symptoms together seem like a different cause is at work. It's possible that allergies are underlying an infection, e.g. Sinus infection. If persistent, this would need evaluation.
If severe. An allergic reaction may include these symptoms.
Insufficient data. Please repeat your post but this time specify what kind of allergies you mean: Drug allergies, food allergies, or environmental allergies. If environmental, try to specify: House dust? Mold? Pollen? Other? Also bear in mind that a lot of what are popularly called "allergies", really aren't true allergies. Have you seen an allergist and been tested?