That's a lot of questions! You may want to consider reading some of the material at
http://www.ROTHIRA.COM which has a combination of stories on applicability, tax payer options, regulations calculators references, etc. Another source of information is IRS Publication 590 "Individual Retirement Arrangements" which covers regular, educational and Roth IRAs.
Which is "best" is a function of your age, marital status, annual income, current and future tax brackets, other investment options, retirement goals, financial knowledge, etc. Two of the key benefits of Roth IRAs are: no taxes on standard withdrawals and no mandatory withdrawal schedule. Some of the limitations include: maximum of $2,000 per year contribution, income ceilings, restrictive treatment for married filing separately, and possibility of future changes in rules.
You are eligible for a Roth if your modified AGI (adjusted gross income) is less than $110,000 (single) or $160,000 (married filing jointly). Roth IRAs contributions are not tax deductable.... in some cases regular IRA contributions are deductable. Yes, you can contribute to a Roth regardless of what you are doing with your 401K.