Can I contribute the max to my 401k and contribute to my IRA in the same year?

Answer 1

Yes, you can always contribute to an IRA. The deductibility of the IRA depends on your marital status and income levels because you a participant in an employers plan.
If your income is too high the IRA contribution would be non-deductible. You should then also look at do you qualify for a Roth IRA. The earnings on a non-deductible IA are taxable in the future. The earnings on a Roth IRA are not taxable in the future.