I'm assuming that by saying "I'm a US resident now" you're referring to the residency determination for tax purposes.
Should I file a return in the US even though there is no income here ?
Yes. US taxes its residents for tax purposes (which is not the same as residents for immigration or other purposes) on worldwide income.
If yes, do I get credits for the taxes I paid in India. What form
would I need to submit for the same ? I am assuming this form has to
be issued by IT Dept in India or the employer in India ?
The IRS doesn't require you to submit your Indian tax return with your US tax return, however they may ask for it later if your US tax return comes under examination. Generally, you claim foreign tax credits using form 1116 attached to your tax return. Specifically for India there may also be some clause in the Indo-US tax treaty that might be relevant to you. Treaty claims are made using form 8833 attached to your tax return, and I suggest having a professional (EA/CPA licensed in your State) prepare such a return.
Although no stock transactions were done last year, should I still
declare the value of total stocks I own ? If so what is an approx. tax
rate or the maximum tax rate.
Yes, this is done using form 8938 attached to your tax return and also form 114 (FBAR) filed separately with FinCEN. Pay attention: the forms are very similar with regard to the information you provide on them, but they go to different agencies and have different filing requirements and penalties for non-compliance.
As to tax rates - that depends on the types of stocks and how you decide to treat them. Generally, the tax rate for PFIC is very high, so that if any of your stocks are classified as PFIC - you'd better talk to a professional tax adviser (EA/CPA licensed in your State) about how to deal with them. Non-PFIC stocks are dealt with the same as if they were in the US, unless you match certain criteria described in the instructions to form 5471 (then a different set of rules apply, talk to a licensed tax adviser).
I will be transferring most of my stock to my father this year, will
this need to be declared ?
Yes, using form 709. Gift tax may be due. Talk to a licensed tax adviser (EA/CPA licensed in your State).
I have an apartment in India this year, will this need to be declared
or only when I sell the same later on ?
If there's no income from it - then no (assuming you own it directly in your own name, for indirect ownership - yes, you do), but when you sell you will have to declare the sale and pay tax on the gains. Again, treaty may come into play, talk to a tax adviser. Also, be aware of Section 121 exclusion which may make it more beneficial for you to sell earlier.