Here is the form your boyfriend needs to file to obtain an extension from the IRS: http://www.irs.gov/pub/irs-pdf/f4868.pdf
Here is the form for the State of Washington: http://dor.wa.gov/Docs/forms/Misc/AppExtenTimeFileEstateTaxRtrn.pdf
However, your boyfriend needs to estimate his taxes now, and pay those.
(Q1) How can he estimate his taxes - is there a "how to" website with instructions?
(A1) There's always TurboTax (www.turbotax.com) or the IRS itself (www.irs.gov) , but most of the time, people estimate taxes that are due based on their previous years' taxes.
(Q2) Can he postpone paying his 2010 taxes, seeing as he has maxed out his credit cards to pay for previous years' taxes?
(A2) Not really, but he can ask for a payment plan. Here's how: http://www.irs.gov/newsroom/article/0,,id=181096,00.html
(Q3) Does he have to report his Roth 401K?
(A3) If he's contributing, he has to pay income tax on what he contributed (if he's an employee, he's already done that). If he's getting a distribution, he should have gotten a 1099-R and needs to report that - although he won't be taxed on it.