what I meant by saying your year starts from the time you entered USA is that you are effectively excluding any Non-US sourced earnings till you entered USA -- thus your UK salaries prior to May are left out ( and therefore also not eligible for tax credit). Thus you say NO to if you earned an income in another state ( this for state tax purposes means another US state ); you also answer NO to havng lived in another state -- because you were not a US person / taxpayer till admitted to the USA.
Passive earnings such as interests, dividends etc. are generally allocated to the whole and for simplicity sake assumed to be posted at the end of the year and thus would be taxable / reportable to the USA ( foreign source and therefore any UK taxes on this would be eligible for tax credit ). ISA is similar to IRA here in the sense ( only) that it is tax-advantaged savings account -- but not as well regulated as the IRAs. It is probably safest to report income from these as savings account interest and because of being non-taxed , US will tax this only ( However, suggest perusing the US-UK tax treaty to see if these are covered and if any treaty assertions can be made --- I will also look this up ).
