Yes. After every heavy rain storm it would be a good practice to open the access cover and make sure no debris was lodged in between the flapper and body, which would not allow the flapper to close. If there are not any storms in a 3 month period of time, it is also recommended that you inspect the flapper to make sure that no debris from normal use is lodged or stuck between the flapper and valve body. This will ensure the valve can seat properly if a storm passes through. 
No. The flapper would remain in an open position without any backflow protection.
You should contact the barrel manufacturer for their recommendations.
You can disconnect the hose and insert the red plug. 
If you disconnect the hose and insert the red stopper plug into the outlet of the diverter, the minimal amount of water that freezes inside the diverter body will not damage the diverter. The diverter is designed to redirect a small amount of water into the outlet as it spirals through the downspout. Once it is capped off a very small amount of water will be trapped and able to freeze. This small amount of water will have plenty of room to expand as it freezes without causing expansion damage to the diverter. 
100% silicone caulk is recommend. There are many conditions where plumbers putty could cause product failure and finished product staining, please refer to category #4 FAQs for these applications.
After the finished height of the No-Caulk Shower Drain is determined as described in the installation instructions, the finished vertical drain height will be ¾” below that. Contact our customer service department and they will be happy to send you a copy of the instruction sheet and exploded view drawing. 
Stainless steel
#10 x ¼” 
The Closet Flange Spacer Kit is used when the finished floor of your bathroom is higher than the bottom of the existing toilet flange.