How do aviation engineers ensure that the landing gear opens every time, without fail?
The short answer is extensive testing and backup/manual over ride systems. In reality there is not a whole lot that can go wrong, landing gear systems are fairly simple in design.  

This varies a bit by airframe but most landing gear systems are pretty much the same. Basically every aircraft out there, from a single engine Piper Retract all the way up through a 747 has some form of manual gear over ride system. You can read about that in this answer here. So basically if the main system fails (and it happens) they have some kind of manual over ride to force the gear down. Granted there can be cases where the manual over ride also does not bring the gear down but you can only be so redundant. Some gear is also held in place positively, in other words there is pressure on the system holding it up so that should the hydrolics fail you dont need the pressure to get the gear down. Often the gear is oriented so that gravity and aerodynamics can deploy it.   

Fixed gear is generally not a great idea on anything bigger than a small trainer. Fixed gear adds drag at the cost of a simpler airplane. You can read up on a similar question here.

I dont think lighter gear is something they are looking into to solve the gear deploy issue. Generally speaking you want the gear to fall down in the event of a failure so a little extra weight is not the end of the world.