Can I run when I am pregnant?

I have recently started to stretch to start learning yoga and I have become sore in my muscles, and was wondering if I am sore the next day after stretching, is it okay to stretch the next day when I am still sore?

1) When I do a 3-mile or 5-mile run, I run for time and try to finish with nothing in the tank. The closer I get to the end, the more I push myself, because I know I don't need to sustain the effort much longer. When I stop running, I suddenly get very light-headed and dizzy. It never happens while I'm running. I walk briskly while I'm warming down, but that doesn't prevent it. Why does this happen? Is it dangerous?

2)  Sometimes after jogging a while, or cycling a great distance, my head begins to spin and I feel as if I'm going to pass out. Is it normal to have feelings like these, and if so, how intense should these feelings be?

I have two questions:

(1) What are the benefits of jumping on a mini-trampoline?

(2) Are there any benefits to using a hula-hoop?

As you can probably see, I'm looking for exercises that are fun.

It's been about three months since I worked out regularly. I find that lifting for strength (i.e. 80% of max for 5-8 reps) causes me to feel nauseated about 3/4 through the workout sometimes, so that I can't bring myself to finish. I took a weight training course last semester and was affected the same way every once in a while. I warm up, stretch before and after, breath when I lift, drink plenty of water, take care not to eat 1 hour before working out, skip a day between workouts, don't lift more than I can handle (I reduced the weight from what I ended on in the class to a seemingly suitable weight. I got a 98 in the class incidentally). What's going on?