I've been on both Voyager and Adventure of the Seas (both of which are the "original" sister ships to Explorer before the ships were redesigned in favor of using more glass and less steel for the balcony rooms). In any case, the Explorer is no different in terms of design. The Explorer of the Seas entered service in late 2000 (October if I recall correctly). It's design maintains the normal amenities of the RCCL Voyager Class...Rock Climbing, Ice-Skating, Basketball...well you get the picture...It's currently the third largest cruise ship worldwide (sharing its title with the rest of the Voyager Class).
Royal Caribbean as a whole has implemented a curfew for everyone under 18 enforcing it with rentacops. Different people have reported that sometimes this curfew is enforced, and sometimes it is not; depending on ship. People you meet onboard will vary depending on the time of year. Since you're sailing in July, you shouldn't have much problem finding people onboard. You can guarantee that you'll never be bored onboard the Voyager Class...it took me three cruises to fully try everything out onboard the ships, so if you don't get to something (like rock-climbing or ice-skating), don't be surprised.