The other SDK's mentioned are also Lua-based and work much in the same way as the Corona SDK, however, Corona has had lots of time to mature, and is co-founded by Carlos Icaza and Walter Luh, both of whom are pioneers in the mobile industry (they have worked for Macromedia, Adobe, Apple, the list goes on, etc. etc.)... In fact, they've had their hands in industry-leading software that many of you probably use on a regular basis (Illustrator, Photoshop, the list goes on...)
The Corona SDK is also growing an amazing pace, so you can be confident that it's going to stick around for a while.
And to answer your final question, no, you cannot build for distribution using a trial membership with Corona. The trial, however, does not expire.
