I work for a Private Company in NYC.

My Employer has a 401(k) offering and by the end of the year I'll have made about $ 4K as personal contributions. My employer matches dollar to dollar for this contribution.

1) Given the above information, can I make the additional contribution of $6 K towards an IRA account?

2) If so, does it have to be Roth or can I put money in traditional IRA and how do I make it come from pre-tax income?

3) From what I've read, I cannot claim deductions for this contribution because I'm the head of the household and I earn more than $74,000. Have I read correctly?

4) If I put my money into traditional IRA (in which I already have some pre-tax funds from a from an earlier 401(k) rolled over into this IRA), and I cannot claim deductions, will I be taxed on the contributions I make at the time of withdrawal? Or would it just be the earnings over this money?