cardiovascular exercise and weights on same day?

It's fine. 2-3 times a week I train in a public gym with co-workers in do warmup circuit & biking or running before doing a fairly fast-paced weights routine (minimal rest between sets). At home twice week I do powerlifting style training and the cardio comes after.

Yep! Mon/wed/fri I run first then lift.

I cardio in the morning, lift in the early evening.

Of course it is, as long as you take the overall volume and intensity of training into consideration. I typically lift prior to cardio, but do what works for you.

I run at 5:30 a.m. and lift around 9:00 a.m. (I do both on the same day 4 days a week).

Depends a lot on intensity and what your body is used to. I once went to a strength-based conditioning class and felt great after that was over, so I immediately ran 3 miles. I was used to running that distance frequently, but not used to the class. I could barely walk for days after that! Now I try to get in a walk on my strength training days, and save the running for the next day.

Of course you can.

You have to put some thought into what you're after. Because both types of workouts are going to make you fitter in the long run, but they're going to take something out of you in the short term. It'll be up to you to figure out how to manage that to achieve your goals.

Most of the year, I ride a bike, and I'm pretty serious about it. I like to get a ride in after work, usually just a loop around the lake, but Tuesdays I do hill repeats. Those workouts are more regimented and structured, I have power targets I'm trying to hit, and if I can't, there's no point to the workout. This is something I would do before lifting when they both happen on the same day, but when it's just "ride for an hour and have fun" then lifting comes first, because that's not the type of ride where my performance is of the essence.