Most good running toilet will recommend replacing a gate valve regardless of its condition. The time to discover if it will work is not during a flood in your bathroom. If you have it replaced with a ball valve then check your water heater and laundry valves, too. Have them replaced at the same time with premium ball valves. Ball valve laundry bibbs make it easy to shut off the water to the washer after each use which may help to prevent floods in the future.
Visually water line repair examine the frozen pipe for signs of damage including cracks holes or breaks. Begin your quest in the areas that are located closest to cold area such as the outer walls and crawl spaces. The holes can be as tiny as a pinprick, so inspect the pipe closely.
After you have the stems out you should be able to find the washer on the "inside" end. If it is nicked, torn or brittle it is likely the cause of your drip. Even if it looks brand new, go ahead and replace it. You've already come this far. You can get replacement washers at almost any hardware store. Sometimes you may want to replace the whole stem, especially if the handle end is stripped out. It's best to just take the stem with you to the store and see if you can match it up. Most Do It Yourself stores have replacement stems for many popular brands. If your valve has a center diverter valve to switch the waterfrom the tub spout to the shower head the same process applies. Many times it is easier to replace the diverter stem than to repair it. This really depends on the design of the stem.
Getting advice from someone who has not made any money online is like asking a plumber to shoe a horse when they have never done so. Why in the world would you do this?
The water line repair most likely damaged your electrical outlets and lighting fixtures. Have a qualified electrician come in to evaluate and repair the electrical.
When doing the install on a water heater, keep an eye out for unconnected pipes. A commonly missed pipe is the one that leads out from the area for drainage. It is probably a recirculation pipe; that helps your water remain heated without wasting too much water.
Especially with older plumbing systems, a leaky pipe is like an alarm, signaling that other pipes may also be on the brink of failure. To get a grip on whether your plumbing system can last, a professional plumber may send a remote camera through your network. If any pipes are about to break, the camera will give you a heads up. If your entire plumbing system is outdated and weak, it may be best to simply replace the whole thing. Although this can be a costly enterprise, with a price tag of at least a couple of thousand dollars, the upside is that a new sewer line will reliably perform its duty for decades to come.