As others have pointed out, you have to pay to send messages.
There is a message limit, but I can't find it described/specified anywhere, but it's not many, something like 3-5 a day. Once you've hit your limit you can keep typing messages and hitting send, but they just disappear (undelivered) with no warning. If you attempt a like/heart/etc after the limit it does warn you about that.
There are certainly some real people there amongst the dead / fake profiles. Zoosk is probably no better or worse than most other real sites in that regard. The constant upsell is annoying though (Message receipts $ - Profile boost $ - Set visibility $ - Extra conversation$ - etc)