Yes. In the break out of the income, the "Jan - 31 Aug - Lived and worked in NY" period means all the income received during those 8 months are NY taxable.
On the 401K question. That is all handled on your W2s. Boxes 1 and 16 are already reduced by the pre-tax contributions. Once you have figured the proportion of time working in a state, you will multiply the taxable wage amount from your W2 (already reduced for pre-tax contributions) by the proportion to arrive at the portion that belongs in that state.
Yes, it's better to do all pre-tax contributions while you're in a higher tax state. That means you will save money on future taxes.
Here's an example to illustrate. You earned $1000 income in NY that would have been taxed at 6% ($60 tax) but instead you contribute to your 401K so it is not taxed ($60 in your virtual pocket). If you had earned that same $1000 in VA at 5% tax rate, that would have been a ($50 tax); $50 in your virtual pocket.
Now in retirement you live back in a state with a 6% tax so the 1000 distribution will be taxed $60 and if the contribution was in NY you'd have $60 in your pocket to pay it. However, if the contribution was in VA you'd only have $50 in your pocket to pay it.
@ObjectiveOriginal
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