83(b) election is for restricted stocks, not options, so my answer assumes exercise at vest/at grant (early exercise).
Will I have to pay tax on (2000 * 8 = $16000)
Will it be a regular income tax or AMT or a short term capital gain?
You have no gain. You vested at $10 and sold at $10, you got a wash. The $16K you mentioned earlier is the benefit you got from the company, which is not a gain but your salary and is taxed as such (including FICA etc).
Also, I read that 83B does not make sense for vested stocks
In the above case, can I file 83B for the unvested 1000 stocks?
No, you can only file 83(b) election within 30 days from the grant.
By not filing it, you ended up with $16K being taxed at vest time as your salary (i.e.: at marginal rates). Had you filed 83(b) election on time, you'd pay the tax on your benefit (the $2 per option, if you didn't have to buy them), but all the gains on vesting would be capital gains (likely long term). That ship has sailed, for that particular grant.
Since in your case you can exercise the options, it is not as bad as it could have been. Consider a case where you got 1000 options at $0.01, they vested at $1000, you exercised them to get the stocks and you couldn't sell any (not yet public, can't sell privately, etc). You'd be taxed on $1M when you never actually received any cash income, and you'd have to chip out $300K on taxes on income you never had. By the time you could sell, the stocks can fall, say to $100, leaving you with hundreds of thousands of capital loss that you cannot deduct, and hundreds of thousands of taxes owed which you have no money to pay. That led to a lot of problems for people during the 90's .com bubble and the subsequent crash.