Is the generally accepted belief in the science community, that if one sits in a spaceship and move away from Earth where r (distance between earth and my ship) is continuously increasing, can one keep going forever?
Yes. There are no edges of the universe that have been observed.
The standard cosmological models favoured by observations (open or flat universes) allow you to move outwards indefinitely. Closed universes are like the surface of a sphere, and you would eventually return to Earth unless the expansion was too fast; the same is true for the models with nontrivial topologies - but these have no evidence at present.