Can anxiety ever by beneficial?

Maybe. Well we think of anxiety as being counterproductive usually. I guess it depends on how you think about it. If being anxious about a test in school causes you to study more and you get an a, then i guess you could say it was beneficial. Interesting question!
Mindfulness. To get rid of anxiety try reading on mindfulness. It works and you don't have to take any medication.
Normal Anxiety. Yes normal anxiety helps us to be on time, keep our life in check, be safe while we drive and be aware of our environment so we are not subject to dangers when its beyond our control it causes disability and needs treatment.
Absolutely. Anxiety serves many useful functions most notably to serve as a warning system to any perceived threat. The reason your ancestors survived and procreated was because they had anxiety systems that allowed for survival. Anxiety is a finely tuned biopsychosocial emotion which has been honed by evolution.
Yes. Anxiety is necessary to avoid dangerous situations. In fact, a lack of anxiety is just as dangerous as too much anxiety and can lead to poor decision making and excessive risk taking. Individuals who have no anxiety can do themselves a lot of harm. What's more, if you teach yourself to channel your anxiety, you can use it to help you focus on the thing that scares you to get it done.
Yes. Within limits, anxiety can keep you moving forward. For instance, if you're giving a talk and you're a little (not overwhelmingly) anxious about it, you may put in more time researching & practicing, so that ultimately, you communicate clearly to the group. They get your intended message. You can then relax, with job well done. Too much anxiety though, & you can't even start. So, within limits.