Does a shower valve need replaced if the water in the shower is lukewarm and the water in the kitchen at the same time is hot?

For Moen, there is a part called a "posi temp" and this can be replaced to manage the hot water. You may need a specialized tool called a puller. There is an amusing You Tube with Steven Lavmoniere that shows the process to do this.

Maybe. If it is a Moen or other type of single handle shower valve, try changing the cartridge first. If this doesn't work, you need a new shower valve.

ANS2 - Shower valves of all types will clog up with any bits of sediment or rust in the system. This is very common. Take the valve apart and check carefully inside.