Hi and welcome to our site!
When the corporation is created - and founders are making contributions in exchange for stock - the income is generally NOT recognized as long as the stock is not sold. Thus - as long as you keep shares - the appreciation of shares does not result in any tax liability. When shares are sold - either back to the corporation or to investors - the capital gain is recognized.
The issue might come when shares are given as a compensation of services - for instance for employment. In this case employees recognize income based on the fair market value of shares - and such income is subject of ordinary income tax and employment tax.
The issue is that according to section 83 income is only recognized he stock vests. However - if the section 83(b) election is made - the founder/employee recognizes “income” upon the purchase of the stock (the difference between fair market value and the price paid). That income is taxed as wages, but when shares eventually are sold (after they are vested) - the gain will be taxed as a capital gain - not as wages.
First of all - as founders - you may have all shares vested - and establish the basis according to initial contribution. Then - when shares will be sold - the gain will be treated as capital gain - and there is no need to make section 83 election.
Generally - the scheme you proposed is good for key employees who are not founders and founders want such employees to be attached with the vesting schedule.
Specifically for your questions.
1. There is a founder with a SSN but now an Indian resident who does not file taxes in India. Does he need to file taxes in US if he elects 83(b) and quotes their SSN.
To make section 83(b) election, you have to send a letter to the IRS within 30 days of the grant being made. Here is a simple letter - http://www.irs.gov/irb/2012-28_IRB/ar12.html#d0e3012
There is no requirements to file the tax return just to make an election - unless the person is required to file. Yes SSN must be included - the SSN serves as a tax identification ID.
2. The founder without a SSN, electing 83(b) does he need to file tax returns in US
Again - if the tax return is not required - no need to file. However - the person would need a tax ID - and for the nonresident alien who doesn't have any tax ID - Section 83(b) Election letter must be filed as an attachment to application for ITIN - form W7.
3. What would be FMV of the stock for the tax calculation purposes. Purchase price or some other method?
There is no specific method requirements - any reasonable method may be used.
In general - you need to estimate the value of the corporation. For the corporation just recently created which doesn't have any valuable assets - the fair market value may be estimated as the total amount contributed by founders. That value may be divided by the number of outstanding shares - and you will have an estimated value of each share.
The benefit of using section 83 election - to treat expected gain as a capital gain - and not as wages - with lower tax liability.
Honestly - I do not see how that election would benefit in your situation...
Let me know if you need any help.