Multiple State Filings

For my wife and I, 2021 is complicated regarding how many states we need to file in.  I purchased the Turbotax Premier desktop package plus 3 additional state filings with the understanding that the product would give us clear guidance on the filing process, but I’m not so sure about that.  To summarize my situation:

  • My wife and I started 2021 living in DE; then on 6/15/21 we sold our DE home and moved to NJ where we rent a home; we are married filing jointly
  • I started 2021 working for a DE based firm; on 3/29/21, I changed to working for a NJ based firm; for the DE firm, no NJ tax was withheld (which I believe is correct since I lived in DE while working there); however, my NJ based firm only reported state wages and withheld state tax for NJ, but I lived and worked remotely in DE for about 2.5 months with them; I requested my employer provide me a corrected W2 showing my proper DE income, but they said they cannot because they don’t have a legal entity in DE
  • From 1/1-1/6 my wife was not employed; she started employment on 1/7/2021 and worked from home 100% because her office in Philadelphia, PA was closed due to COVID, and remained as such for her entire time in 2021; On 11/1/2021 my wife transferred offices from Philadelphia to New York City, NY, but continued to work from home 100% out of convenience offered by employer due to COVID
  • My wife’s employer reported income and taxes for DE, PA, NJ, NY, and Philadelphia

Questions:

  1. Where do we need to file tax returns?  I see it is possible for DE, PA, NJ, NY, Philadelphia, and New York City.  But considering my wife worked 100% remotely in 2021, perhaps some locations we don’t owe tax, but I don’t see any such option for that in Turbotax ;if we need to file in cities Philadelphia & New York City, I don't see such capability in the Turbotax Premier product based on the questions thus far
  2. Which states/cities can I deduct from others?  And do I deduct the taxes that were withheld from our pay, or the tax basis we file, i.e., what Turbotax calculates as Tax required
  3. Do I need to report DE income from my NJ based employer, who didn’t indicate DE wages on my W2 (because I lived and worked remotely in DE with this firm part of the year)?  If yes, appreciate any guidance on calculating DE wages and how to input into Turbotax
  4. My wife’s employer revised her DE state wages; is there a box or something to indicate the W2 is revised?
  5. Turbotax gives us an error/warning concerning our days worked outside NY can’t equal the total days worked; my understanding is the total days worked includes those worked remotely, so considering my wife never worked in NY they are equal and the error seems inappropriate; please comment
  6. NY business income allocation – we aren’t self employed, do we need to complete this?

I know these are a lot of questions, but any general guidance on these topics and filing would be appreciated.