Adjusting a Chinese-made plywood bass

Q: For better or worse I bought a $650 Chinese-made plywood bass. My goals for it are to learn about bass setup and how to play bass then move up from there as my playing improves and budget allows. The bridge that came with it was really poorly fitted, too high and the adjusters weren't installed squarely. The soundpost was also wedged in so tight, misplaced and crooked to boot.  I made a new post and fitted it better. It's 3⁄4" back from the back edge of the bridge and in the same distance as the bass bar. I also did order a new Bausch bridge online and will fit it once I figure out how high I want the action using the original bridge to experiment with. I think I'm after an easy-playing low action but with decent sound.
 
I have found a couple problems.
1) The E-string sounds really dead - little sustain. I'm guessing too low of action and thus not enough downward force on the soundboard? Even before I lowered the bridge I noticed that the instrument has a poor bottom end. A, D & G sound really decent and the E fretted from 4 on up sound ok, but lower than that the sound isn't there. Any suggestions here?
2) Backbuzzing, buzzing between the nut and finger at 4 or so, on the G-string. Not when I play the string but when I release the finger. It didn't do this before I lowered the bridge.
3) A flutter buzz on E at the nut. It's not hitting the fingerboard. It sounds like it's wiggling in the nut slot and creating the sound. You can push on the string at the nut with a finger and the buzz goes away. Do I need a tighter slot or can I widen the slot just where the string enters it and fix it?

A: I don't think that downward pressure is the problem with your E string.  Basses rarely have even projection on all four strings. Normally the G is great, the D less so, the A even less and the E sucks. It is a rare and wonderful bass with a great E. Most bass players just pluck harder on the lower strings. That is what I do. On stage I use a Fishman pickup. It mounts on the bridge and picks up all frequencies equally. I then modify my technique and pluck all the strings the same. Expensive solid wood basses produce the low E better than the plywood ones do. Cheap solid wood  basses, don't work as well as the plywood ones. You have now joined the quest for a good E. Good luck.

A back buzz can be addressed by raising or lowering the nut.
Your flutter buzz on the E string just sounds like loose windings. Your string is bad. It may have come from the factory bad. I have never seen a string buzz from the nut slot being too wide. The string slot should slope downward from the fingerboard end of the slot to the peghead end. If it slopes the wrong way the contact point will be at the back of the slot and the string will mute against the sides of the slot. Lift the string out of the slot and look for the shiny spot. If it is not at the very front of the slot, this could be your problem.
   
Steve Mason