Is it possible to know if you are travelling close to the speed of light if you have nothing to compare your speed with?
Velocity is relative. From your perspective, your velocity is zero. Without windows (or sensors) on your spaceship, you cannot know the difference. To measure your velocity, you have to define a reference point, eg a star, the average velocity of surounding stars or the galaxy center. If you have such a huge velocity relative to them, from you perspective, they are this fast and not you. So you can observe the time and space dilation of these objects, while your time appears to be normal. You ship is an inertial reference frame.

As for throwing the baseball: From your perspective, you have the speed zero, and the baseball eg. the speed 0.5c. A "fixed" observer, which observes you at 0.99c will measure the balls velocity at 0.997c. With those relative effects, speeds don't add up, only kinetic energy does. http://curious.astro.cornell.edu/about-us/139-physics/the-theory-of-relativity/special-relativity/1016-why-can-t-relative-velocities-add-up-to-more-than-the-speed-of-light-intermediate The increased mass is only a relativistic observation, resulting from the kinetic energy (relative to the observer).