The faucet still works but the handle is stripped? You can get new handles that will work on any faucet. They have a square adapter that attaches to the faucet stem with a set screw and then the new handle fits on the square adapter.
Also deal with a plumber supply store rather than "Big Box" store, they will have some odd parts, not available from the big chains.
Worn gasket inside slipping into and out of position too easily. The packing gland (nut) needs to be tightned slightly
what is the GPM rating from the old to the new the lower the GPM the slower the water. Sometimes there are restrictor discs (washers).
Remove the handle, again. Turn the water off at the outside valve and turn another faucet on to relieve the pressure. If you look closely at the stem that the handle screws on to, it has a square area on it that you can put an adjustable wrench on and turn it to the left. The stem will or should come out. There is a seal at the far end that needs to be replaced. Take the stem and all to a local hardware house and they will have a replacement for under two dollars. Now, reinsert the stem and tighen to snug and replace handle. Turn the water back on outside and try it.
Your hot water line needs more insulation probably. It sounds like your hot water is cooling before reaching that faucet. It may be that the one faucet is not able to turn all the way to hot until you adjust the faucet (usually in the handle) of a 10 year old or newer faucet.
A wrench icon appears on your cars dash when the engine needs attention.
Faucet needs repaired.
You have air in your pipes and it needs to be flushed out.
needs an o ring in the hose
if it is a single lever faucet the cartridge needs to be replaced. check the supply valve under the sink first,
A lot of them resemble a large screw with a fiber/rubber washer at the bottom. The washer needs to seat with the valve "seat" at the bottom of the individual handle (hot or cold) the "seat" is usually the size of common Allen wrenches. But the leaks usually involve the washer not the seat. There is a drawing linked below.
It means your engine needs attention.
Leaky Moen faucets can usually be repaired by competent adults. Shut off the water at the valves below the sink, then flip off the plastic disc that has H or C on it. Under that is usually a Phillips screw, undo this while grasping the handle, then pull handle off after the screw is out. Now you will see a large nut holding the stem in, that needs to be removed. This is often 3/4 or 7/8 , but a crescent wrench is the handiest tool for it. When this nut is off gently pull out the stem. This will have either a rubber washer on bottom, or a plastic cartridge. Take this to a store like Home Depot and match it. If it is a Moen faucet with as lifetime warranty, HD usually has a case of Moen parts which are free. -Replace everything in opposite order.