I am in same situation too. Plz let us know if anybody has any past experience. Any inputs will be really appreciated.

Green card application has nothing in relation with h1b except the fact that your h1b will allow you to work while your green card is in process. If you have masters degree and your job requires a masters degree you are qualified to apply for eb2.

 What about the salary requirement ? Does it have to certain amount or it depends on the city and State i live...If i get little above PW, it should be fine right ?

Racheeta,
Is it possible to file Green Card without H1b (if employer is willing) ?
H1 has nothing to do with filing green card, but if the H1 sponsor and green card sponsor is same company it is a plus point in the sense that  you can show the company is able and is paying the minimum salary required to be paid to you. In other words, if you are sponsored directly for green card your company should submit proof of financial ability to pay you the required salary i.e. tax return, financial statement etc. whereas if you are already in H1 and in the payroll you can only show them your pay stub.
am i eligible for Eb2 or Eb3 ? I've bachelor's degree from US as well. .
From what you have said you are eligible for EB2. Be advised that EB2 processing is faster (if everything goes well it will take less than a year for a Nepali national) whereas  EB3 takes lot of years.
Is there any minimum salary requirement for filing EB2
Yes,  this depends upon the state you are filing from and the position (post) for which you are filing. You can find the minimum salary from  Dept. of Labor's website(wage determination chart).

Hope this helps.

 EB2 is applicable. The best is to start the processing of GC once you join  the company with OPT card. With that, ur company's financial ability to pay you will be reflected thru ur paycheck and if the prevailing wage is larger, the company's ability to pay you after getting GC will be reflected from company's tex return docs. The wage that the company pays you at current does not necessarily be the equal or greater than the prevailing wage. Only for position advertised for GC, the payment shoulde me equal to or more than prevailing wage. 

While the GC processing is going on, you can apply for H1 (during normal H1 application season), since the total processing time is over 1 year from the time u start the process and ur OPT will be for 1 yr only.