I have an old JB Player electric guitar. It has a wammy bar (black). Anyway the part that the wammy bar goes into that holds the strings down at the bottom of the guitar is not good any more. I think there is a problem with the springs. I think they might just be worn out. So the action of the strings is very bad. Where could I get a replacement / new part that would fit my guitar?

I Am Assuming the String Have A Ball On One End. Those are to Go Into The Holes in the Bridge of The Guitar.
Have you ever put strings on an instrument?
What Kind of String Are On The Guitar Now?
Different Colors On The Ball For Different Gauge String, Here is a link to How the String are Made. Scroll Down To The Section That Deal With The Nuts And Bolts and Ball Ends Of Things
https://www.ernieball.com/guitar-strings/electric-guitar-strings/electric-tone-packs
If You Bought 10 Packs Better Learn How To Use Them Or Trade Them In for the Right Ones. ......~~~~*BB

One of the best was to keeping your guitar in tune, is to also string it correctly and use new strings . Make sure the first winding of a new string around the tuner post goes over the exposed tip of the new string. The rest of the windings go under the exposed tip of the string. This will keep the string clamped firmly in place. Use 4-5 turns around the post for unwound strings, 2-3 for wound strings, in a downward spiral towards the bottom of the post as shown in the photo.-Tom, 30yr player.

The electric guitars without the floyd system usually have the wire gauge of 10-46 (10 being the thinnest and measuring just 0.010 inches)
The gauge goes from: high e - 10, B - 13, G - 17, D - 26, A - 36, low E - 46.
Strings D, A and low E are wound and have a gold look, while G, B and high e are plain and have a silver look.

The internal workings of the guitar - pickups, potentiometers, switches are not grounded.
Very common.

I am not sure if you know what the "nut" is... it is the little bar that the strings go over after they leave the tuners. If this is what you are refering to, the "nut" just rest at the end of the fret board and is held in place by string tension. You orient it so the one flat side goes down and rests on the neck and the other flat side rests agains the fret board end. You USUALLY do not adjust this unless the string height is wrong at the end of the neck nearest the tuners. Essentially you just seat it and then the string tension holds it in place... The only adjustment available is to lower it by taking material off by sanding OR to put a few layers of parchment paper beneath it.
Hopefully this is the nut you are talking about and not the truss rod adjustment which, unless you are experienced, you should NOT attempt to change. If you have disturbed the truss rod, take it to a guitar shop for repair.

Look for something related to the whammy bar causing unstable tuning. The only other thing is string QUALITY and gauge. Use the recommended strings for the guitar.

Turn down the treble gain and mid gain... you don't need it for a bass. Prevent the guitar from "hearing" the output of the amp directly. The guitar strings make a good microphone.

Possible problems include defective volume control or broken wire OR improper wiring.

Volume controls can have a broken resistance element and fail to go to zero volume.

whammy bars are available at musiciansfriend.com it looks like you have a strat copy they will need to know that

First, I don't know how long you've been playing guitar but you need to make sure the strings aren't old and/or not kept clean. The oils and skin cells from our fingers will cause strings to break down in there elasticity, therefore causing them to lose there retention (eg. memory). If you have a locking system with floating bridge then make sure your locks are tight, but not to tight as to strip or break the screws. Next, if you have a cheaper guitar, like in the $250 range, you will experience this more often than not, especially if you don't have a locking system. But just remember that guitars have to be retuned all the time (just watch live video of guitarists like Jimmy Page and Angus Young, etc.) if you play a lot and really play the instrument to the fullest (eg. Dive Bombs, EVH Horsie, Pitch Bends, etc.). Also, when you put on new strings they need time to stretch before they find that place where they retain their memory so it's a good idea to play and stretch the strings using various techniques like bending and whammy (EVH has been known to boil his strings to aid in this). Last, but not quite the least, if you find your guitar going out of tune after just a few minutes and after all my suggestions then your guitar may have a problem with its INTONATION, which you'll need to take it to a guitar technician which won't cost much and you'll be very happy with the sound. One last thing to remember, if you have a cheaper guitar without locking system they're really not capable or designed for using the whammy bar that comes with most of them---this is just a feature for helping to sell the guitar because everyone wants a whammy bar---the guitar will go considerably out of tune everytime it's used. Hope this long explanation helps.