Will there be any special events on May Day?
What are closed( sights,shops etc) on that day?
Although Labor Day (May 1st) is a bank holiday, it really shouldn't effect you as a tourist. Restaurants, public transportation and many stores will be open as usual. Were a national strike to be announced, things might change, but in general Spaniards take their vacation days too seriously to muddle them up with politics. (I can't remember any major strike having taken place on May 1st.) On the other hand, if you are in a biggish city it might be fun to participate in a rally -- they are usually accompanied by a concert, picnic, etc. The big union web pages (ugt.es; cnt.es; and ccoo.es) will probably provide information as the date approaches.
Good question Faye - I wondered the same since its a National Holiday. I will be in Sevilla that day myself! Wondering whats open (may be a good day of lots of old town walking and cafe trying - or a beach or mountain-monastery tour day for Barcelona).