Can cellulitis cause flu like symptoms?

Not typically. Cellulitis is defined as a localized skin infection which should be diagnosed by warmth, redness, tenderness and possible swelling. Flu like symptoms would include generalized body aches, fever, fatigue, and possible cough or congestion. Flu (influenza) is a virus while cellulitis is typically bacterial. However if cellulitis spreads to the blood then some flu like symptoms could be possible.
Yes. Systemic symptoms of cellulitis maybe from septicemia (blood infection) or the immune system response. Nausea, vomiting and chills are typical with elevated temperature and blood pressure changes.