(1) What does it mean when E. coli is lys+ or ser-, or anything similar to that?
Lys + usually means able to make its own lysine. Ser- usually means unable to make its own serine. Lac+ usually means able to break down lactose. In general, the "+" means able to synthesize and/or breakdown (depending on context) some compound; the "-" means unable to carry out the necessary steps in metabolism to use and/or make the substance.

(2) What is progeny?
progeny = offspring or descendants.