Can I pursue a PhD while working as an Instructor/Lecturer?
Most universities are fine with having PhD students working as instructors/lecturer/teaching assistant at the same time, and it's actually quite common. I have personally been teaching at undergrads level while doing my PhD, and most of my friend who did a PhD were in the same situation. 

However, it depends on the amount of hours you are spending a week with teaching: if it's taking all of your time, you might not be able to do research in good conditions, and it might be hard to find a professor that would agree to supervise you if you're not available to work on your PhD. Basically, if you combine a part-time teaching/part-time PhD, that should be fine, but if you combine a full-time teaching with a part-time PhD, that might not reasonable. 

Concerning where you should apply for the PhD, in general, you can do it in a different university than the one where you're teaching. However, in some cases, it might be more interesting to do it at the same place because you might not have to pay the tuition fees.