Yes, you can maintain both types of IRAs at the same time. You can even make contributions to both types of IRAs in the same year. But your contributions to both Roth and traditional IRAs cannot exceed the maximum contribution limit for all IRAs.
Those who work for a living can contribute to a Roth IRA account. The income must be derived from actual work efforts and compensation in the form of wages, tips, salaries, bonuses and professional fees.
No. The amount you contribute to your 401(k) or other employer-sponsored plans will not be affected by your Roth IRA.