Definitely highly variable. As in any educational setting you've ever experienced, the level of interest and enthusiasm for teaching medical students runs the gamut. Some people love to teach med students. Obviously, getting a resident or attending like that is great for your learning, although you may not enjoy it so much at noon on a day when you're post-call and have been awake for thirty hours straight. Other people will basically ignore you or send you home early so they don't have to deal with you. That's not so great for your learning, but it's nice for your lifestyle.
I would say that on the whole, I had a good experience working with residents and attendings. Of course, I only attended one medical school, so I can't compare what the experience would have been like if I had gone somewhere else. But I did go on two away rotations, and I am now doing my residency at yet another hospital. In every setting, there have been some amazing residents/attendings, and other residents/attendings who have served as a cautionary tale.
Concerning culture, every hospital and every specialty has its own. Case's four affiliates are all very different. University Hospitals/Rainbow Babies is the academic hospital and a tertiary referral center. You can get amazing teaching from leading experts in their fields. Metro is the county hospital, and they do a lot of the indigent care. They're also the main level I trauma center for Cuyahoga County. The VA is your typical government-run facility, with all the good and bad that entails. One major difference there is that almost all of your patients will be male. Cleveland Clinic (CCF) is an enormous group practice with I think around 2000 docs. It's a tertiary care center like UH, but much more surgery-oriented. They have a lot of money to throw around compared to the other hospitals.
People tend to gravitate toward different hospitals depending on what their interests are. The hardcore blood and gore types and the people who want to work with the underserved love Metro. People who want to do surgery and surgical subspecialties are all about CCF. Medicine and peds people tend to like UH/RB. But of course, all the major rotations are offered at all three of these main sites. (The VA is often lumped in with UH, although there are some rotations offered exclusively at the VA.)
It's probably even fair to say that every team has its own culture, largely dictated by the attending as the most senior person. You will see as you go through your clerkships that there is a lot less science in the practice of medicine than you can appreciate right now. Attending A will tell you that he wants a lactate done on every patient, while Attending B will scoff and tell you that there's no evidence to support that. So, what do you do? Well, when you're on Attending A's team, you order the lactates. When you're on Attending B's team, you don't. Any time you start working with a new team, you learn what the attending expects, and then you do it. And that is the art of medicine as practiced by trainees.
Relax. I'm the only person who has any experience with the question you're asking, and I'm still working through bucks' questions. But the short answer is that no matter where you go to school, no, you can't write real orders as a med student. Until you have an MD/DO after your name and a medical license, you can't practice medicine. Period. People who claim they are writing orders as med students are at best having them cosigned by someone who is a physician. And yes, you can do that at the Case affiliates just like you can do that anywhere else if your residents or attendings allow it.
In case anyone is wondering, the orders you write as an intern ARE real, even though you aren't yet licensed to practice independently. I have a medical license and also my own DEA number (which allows me to prescribe narcotics). I also have malpractice insurance. But I have to add the caveat that medical licenses are granted by the state where you practice, and I'm not sure if all states do things the same way that they do them here.