1. Re: patients and problem solving: Complex problem solving is not the sole domain of the internist. Plenty of surgical problems are very complex, and it turns out you are operating on, you know, patients.
2. There is a large chasm between surgical specialties and medical specialties. Even in clinic-heavy specialties like ENT/urology, the"medical" part of the specialty isn't like internal medicine.
In regards to balance, you can make your own practice have whatever balance you want. As a general surgery resident, you'll be doing a ton of operating with minimal clinic, but post-training, it's feasible to have a practice where you're seeing GI patients, doing endoscopies/colonoscopies, and only in the OR 1.5 days/week. That being said, no one goes into a surgical field if they don't like to operate.
How far along in your training are you?