1. I received approximately £15,900 annual living allowance from the EPSRC (meant to cover rent, food, etc.). In the UK, this living allowance is tax-exempt. Do I owe US federal income tax on that EPSRC studentship? If not, what exemption can I claim?
Maybe. Absent a tax treaty that says otherwise, refer to IRS Tax Topic 421 and IRS Publication 970 for more information. I'll briefly summarize the U.S. taxability of scholarships and fellowships.
In general, scholarships and fellowships (whether public or private) are U.S. tax exempt for the amounts used for educational expenses. Educational expenses include tuition, required fees (such as a student fee required for university enrollment), and books, supplies, and equipment required for coursework. You must be attending a real university or educational institution and progressing toward a real degree. (The IRS doesn't use that language, but that's the gist of it.)
Amounts that aren't used for those purposes are generally U.S. taxable but not necessarily taxed. In particular, if you're a Single filer you get a personal exemption and standard deduction that together total about US$10,000. So if, for example, £15,900 is your entire gross income (as a scholarship/fellowship), and £10,000 of that is used for the expense categories that are tax exempt, then your remaining £5,900 is under US$10,000 (at the relevant exchange rate) and you should escape all U.S. income tax.
There may be more tax relief available than the usual blanket personal exemption/standard deduction depending on the circumstances. You have to be at least a bit careful to keep your fellowship/scholarship separate from actual earned income. For example, if your gross income is £15,900, but £10,000 is your scholarship/fellowship and the remainder is paid to you at an hourly rate (for example) as compensation for being a research or teaching assistant, as ordinary wages, then you'd keep those income categories separate. And that's a good thing because there's a separate U.S. tax relief available on earned income called the Foreign Earned Income Exclusion (FEIE) that's probably America's most generous tax break.
Flipping this around, if (unfortunately) you had qualified educational expenses that
exceeded your scholarship/fellowship, there are possible tax reliefs available. IRS Publication 970 explains more about those various tax reliefs.
2. I have an ISA in the UK. Do I owe US tax on the interest from that? If not, what exemption can I claim?
Absent a tax treaty that says otherwise, yes, the interest on that account -- or any other non-U.S. tax advantaged account -- is U.S. taxable (but not necessarily taxed, per above).
Moreover, you'll want to check what you're holding in your ISA. U.K. ISAs can hold various investments, including cash, unit trusts (a.k.a. mutual funds), and publicly traded shares of stock (equities), as examples. Some of these, notably unit trusts/mutual funds, are what are known in the U.S. as PFICs (Passive Foreign Investment Companies) that require special U.S. tax treatment. In particular you'd make what are called mark-to-market elections on your PFICs, meaning you'd determine their value at the end of each calendar year and report the "paper" gain to the IRS using IRS Form 8621. That's a bit complicated, but at your income level that's likely to be rather advantageous in terms of a U.S. tax outcome.
My recommendation is to avoid PFICs, but it's not the end of the world if you've got them already, especially at your income level. Plenty of investments aren't classified as PFICs, so it's fairly easy to avoid the problem, even in a U.K. ISA.
3. I have a non-ISA savings account in the UK. For the past few years, I did not have to pay UK tax on that interest, because I was a student. Do I owe US tax on that interest? If not, what exemption can I claim?
Absent a tax treaty that says otherwise, that interest is U.S. taxable but not necessarily taxed, per above.
In any of the cases above, if a tax treaty says otherwise, you'd use IRS Form 8833 to inform the IRS what treaty relief you're using.
Due note you may have a FinCEN Form 114 filing obligation depending on the total value of your foreign financial accounts (U.K. ISA, savings account, etc.) Specifically, if the total value was at least US$10,000 at any point in time, you're required to file that form. It's due by June 30, so the 2014 report is due by June 30, 2015, for example. If you were supposed to file 2013 and/or prior years, no problem, you can go ahead and do that as long as you have a reasonable, truthful explanation for the late filing. ("I didn't know" is popular, and one of the choices on the form consists of words to that effect.) At present the U.S. Treasury is not imposing penalties for unprompted, voluntary late filing of truthful FinCEN Form 114 reports.
My references to IRS form numbers should not be interpreted to recommend that you fill out those forms by hand, manually. Tax preparation software, even the free stuff (such as the free editions of TaxAct.com and TaxSlayer.com, as examples) is very useful in making U.S. tax filing simpler and easier, and I recommend it.
Finally, be aware that U.S. tax and financial reporting is on a calendar year basis, which is different from what you may be used to (or will become used to) in the U.K.
