Yes, frozen pipes can prevent a toilet from working correctly. If the pipes are frozen, water cannot flow, which means your toilet tank won't be able to refill after a flush. This will prevent the toilet from flushing again. Depending on which lines are frozen, the ice can also block the drain pipe, preventing water from flushing away.

As a temporary workaround, you can manually add water to the tank for each flush. To clear a frozen drain pipe, you can try filling the toilet bowl or tank with warm water and flushing to help thaw the ice. However, the best long-term solution is to unfreeze the pipes to get your toilet back in working order.

An active cleaning agent and a drain snake is the best way to clean a main sewer line. You can purchase a regular or enzyme drain cleaner or make a DIY drain cleaner with baking soda. Use your chosen solution at least once a month or as needed to keep your sewer line clear. 

There are several homemade solutions for clearing a clogged sink that don’t involve pouring harsh chemicals down your drain. Start by pouring hot (but not boiling) water down the drain. This can help dissolve and flush away grease and gunk. A splash of dish soap down the drain can also cut through fat and make it easier to clear the drain. For a more stubborn blockage, grab a plunger and give it a few firm pumps to dislodge the clog.

Air gaps get clogged by a few different means. Over time, food and grime can collect in the air gap, leading to a blockage. Mineral deposits from hard water are a common problem. Mineral buildup creates a film in the air gap and tubing, which can cause flow issues, as well as attract debris. Homeowners with hard water may want to remove mineral deposits regularly to keep the air gap clean and clear.