The fact that your husband has been deported is most likely a hightened risk factor for consdiering whether you should be in the trusted Sentri program. I know of multiple situations where Sentri approval is impacted by family members so it is not uncommon. Also, you shoudl consult with an immigration attorney to determine if there are any avenues to sponsore you husband for residence in the US.
Yes, you do qualify and need to apply based on three years as you indicated you would not qualify if it was based on the past five years. However, you will need to show validity of your marriage if you are filing based on the three year period so you should be prepared to do that at the time of interview.
you should carefully navigate this situation because of timing and the fact that the visa must be issued in the fiscal year that she won. I am also unable to tell if your wife is also in the US as that would impact my answer.
When filing the Form I-90 to request the replacement I-94 card you should specify that you are requesting that they check their records from October and November. Also, it shouldn't be that difficult for you to research old bank statements and itineraries for flights to figure out the exact date of travel. If you know the airline, maybe they can search their records.
Assuming she has not been sponsored for a visa or labor certification previously and eligible for 245(i), she will need to consular process when the visa number is available which coudl be 10-12 years. Whens he departs the US she will trigger illegal presence which is bar to returning without a wavier and it is unclear if she has a qualifying relative for the waiver. If she has more than one year illegal presence she will not be permitted to return for 10 years. As mentioned above, the...
Most flights to Hawaii will be from an interntaional airport which will incrase the likelihood that a CBP officer could ask for a passport even if it is a domestic flight. It is a risk that most don't take since it only takes being stopped one time to change a person's life.