I think you need to build a support network locally. Even if it means going outside the university to a nearby university, you will need mentors, fellow TA's, administrators, and others to help you not just understand and solve the problems you currently see, but to anticipate problems and improve your efforts as a teaching assistant.
Even going outside your department, there should be SOMETHING available at your university. Even if you are the only TA for math for the engineers, other teaching assistants may be able to answer your specific questions even if they are outside the field of the questions.
Point 1): there IS help teaching you to teach; you have to find it. Asking here is a good start, as there are some online resources that you can find with a web search. However, you will need to consult people as many answers depend on the immediate or near environment. (To show off my ignorance, if you have to teach an example of the pigeonhole principle by having students put on or take off hats, and you have a class full of women wearing burkas or some prohibition where wearing hats is socially unacceptable, then my hats example would not be appropriate. I don't know the cultural norms in your area, so stuff I say may turn out to be singularly inappropriate.) You need to develop (and become) local resources.
Point 2) There are obvious goals, they just are unclear and not well formed. An obvious goal is that the engineers need to learn the stuff to either perform certain skills or to acquire material that depends on the stuff you are teaching. If you don't know what they need, find out. However (and I think this is more important) you need to teach them how to recognize what is and what isn't useful, and how to acquire and apply more knowledge. They will be addressing various engineering problems and related problems, and your job gives you an opportunity to address both kinds. They will be better practitioners if they not only can do the calculation/process/design, but decide when and how it should be done, and where they can go to look up the stuff they need to do it. As a brief example, in showing how to do calculations for stresses experienced on a trestle bridge built for a pipeline, they need to consider the weight of both the full and the empty pipes, so they need estimates for the volume and mass of material in the pipe, as well as the mass of the pipe itself. (Borrowed from an incident in which poor design principles were revealed.)
Point 3) In my experience, you can't awaken curiosity on call; it happens or it doesn't. You can try to use some other motivations to help drive the teaching. However, if you can recognize a motivation of your students, state that motivation, get them to agree that it is a motivation, and then show how that motivation drives the lesson you are about to give, that may be a good replacement for independent curiosity. Here you will need examples from the field to provide motivation for you to take this kind of approach.
Gerhard "Local Support Is Very Important" Paseman, 2015.07.13