1. You have the wrong liner. 900 uL internal volume is too small.
If it is true how does this rationalize that 2uL provides disproportionally larger signal than 1 uL. When I image 2uL will be less than double of 1uL signal, right?

Depending upon your solvent and injection temperature you can easily be outside of the gas-phase volume of your liner. I'd recommend using a calculator (Flow Calc from Agilent is free) to calculate your gas-phase volume. If you are outside of the gas-phase volume limit of 900 uL the injector will behave in very strange, erratic ways.

2. . You are running splitless - you will get huge (HUGE) area count swings in splitless. why? If you're trying to develop a relationship between mass injected and area by varying the injection volume go to a low level split injection - use 3-4 mL split flow.

Splitless injection relys on multiple phenomena, including a) not exceeding your liner volume, b) maintaining near-laminar flow, c) proper refocusing of the solvent front on the column, d) reproducible injection speed, etc. It takes great care to get all of these factors balanced; thus, splitless injections are prone to erratic mass transfer to the column. It is much, much easier to work with a low-level split injection (3-5 mL/minute), especially if you are using small ID columns. In many cases you'll find that your mass transfer is actually improved.

3.The HP (Agilent) injector has had problems since its inception. Welcome to a really poor splitless injector. If you're insistent in using splitless injections (I'd recommend highly against it, if you can avoid it, since low level split works so much better) then you probably should seriously think about either incorporating the Restek modifications into your system Before we seriously consider to buy different inlet system we have to know the reason. Would you mind providing some literature? or switching out to something like the SGE injector. So why the injector here solve the inlet problem?

This is a well-documented phenomena - do a search on HP injector discrimination and you'll come up with a treasure trove of resources. The HP injector is a poor splitless injector - by the same token, it is actually a pretty good split injector, and if it is run unmodified, it only works in a split mode due to the way that it is plumbed (this was fixed on the 7890 series). If you insist on using splitless injection then you'd be better off with another injector; again, I'd recommend low-level split no matter what. Your gain in sensitivity between splitless and low-level split is in most cases not large, and using a low-level split makes a multitude of ills disappear.