Woogie is right, stick to TM L96 parts to make sure it will fit and start with the basics. Make sure the trigger box is screwed in completely, check for any loose areas and see if they cant be tightened.
If that dosent help then your going to want to look at your trigger box. Check and see if the sear is worn down.
If that is the case, then you need to replace it, if not test the sear by pushing foward with steady pressure then pull the trigger, the sear will "fall". When you let go it should pop back up or atleast try too. If it stays in the downward postion your going to want to tighten the spring that helps it recoil.
There is only two springs inside the trigger box, one attached to the trigger mechanism itself and the other to the bottom of a bar piece that connects to the sear to hold it in the upright position. Obviously you have to tighten the one indirectly attached to the sear. Your just going to pull the spring down and attach it at a higher point. Just tighten it a few coils at a time until it feels better. Its really easy despite the sounds of it, the harder part is closing the trigger box. Go slow and take your time. All the z-trig sets will need that done to em at some point, the springs just get streched out a bit. And since you bought the gun used, its not a bad idea to do it if its your problem or not.
Like I mentioned before, use the "over-hand" bolt pull method. Pull the bolt back firmly and quickly enough to make sure the sear will catch, but not too hard to hurt your gun. On the otherside of that if you dont put some force behind it you will just miss the sear and have to try again leading to it double feeding.
Grease? I reccomend, white litium grease, I use it on my guns and it works wonders.
That tiny spring your talking about, im not sure on the exact size. But try out a spring from a pen, that might work.
I hope something in here can help you.