It all depends if the Continental uses Lufthansa in Frankfurt for their ground handling. Lufthansa SkyChefs is pretty big, so very likely.

I doubt it though in regards of baggage, fueling and other stuff. You will definitely get there! Also, they will try and focus their strike on domestic and European service and take it easy on international flights. Delays are likely though.

The Unions are crazy. During such a time (airline industry facing the economy and fuel price), the ask for outrageous raises. Well, LH is still making lots and lots money though!