Yes, the surround is the same as foam. Some drivers have textileor rubber surround rings, but these seems to be foam. The magnet keep the voicecoil in the same position wich in is winded and glued to the end of the cone. Sometimes, depending how they were stored, the voicecoil can corrode and get stuck. By gently pressing the cone downwards you will notice if it moves freely.

Avoid quick drying and contact glues. Some of them contains chemicals that will dissolve the foam over time.

Here is a good site with information:

http://www.goodhifi.com/FAQ/Speaker%20repair%20FAQ.htm