I’m not a master plumber but from what I’ve seen is most kitchen faucets of this style have o rings on the stem that can be damaged if the arm gets loose. That plastic ring is a wear surface to allow the arm to move freely. Repair the faucet with a kit if you like a challenge.
Or better, replace with a more modern one. The hardest part of that job is getting the old one out. This requires specialized tools in many cases.
Installing a faucet is a relatively easy if you don’t have shut off valve or supply line issues. That is best left to the pro. Many modern faucets come with supply lines and use a common size 3/8″ to attach to the valve. They are making them easier to install all the time….
It depends upon the leakage. If there is a large leakage problem then I don’t think so that replacing the plastic pipe will be enough. Same problem occurred in my home few day before and I decided to replace it with new plumbing supplies. I bought it form South Coast Sales. Now it is in better condition.