How safe is giving a patient a shot of Demerol & 10mg of valium before a mini face lift? I've read that taking both is dangerous

Mini facelifts are done with local anesthesia and typically some form of sedation or anti-anxiety medication. Dosed properly, these medications are very safe and will keep you relaxed and make for a positive experience. An antihistamine medication could also be used, should you have histamine issues. You should contact your primary care doctor about what would be best for this. Best wishes.

Sedatives are safe when used appropriately. I see no problem with this combination as long as the amounts are not excessive

That is a very good question. But giving a narcotic and a benzodiazepine, like Demerol and Valium are extremely common. This is commonly done in a form of sedation referred as "conscious Sedation". In my facilities where I work, I am required to take classes on Conscious Sedation every 2 years, as well as ACLS, Advanced Cardiac Life Support.
These medications are NOT to be given casually. Because they can cause all sorts of problems. However I use them at least weekly, and have for over 30 years without incident. As long as your doctor and the facility are well versed in using this form, it is very common and very effective.
I hope this helps!