No it doesn't. Your mass increases the faster you go, so that more and more energy needs to be expended to accelerate more. At 50% light speed, you're 15% heavier. At 90% light speed, you're 129% heavier. At 99% light speed, you're 608% heavier. Your mass goes to infinity as you approach the speed of light, which is why the speed of light is unattainable for objects that have mass.

right i assumed low-relativistic speeds. also i got the number of bombs wrong, it's 300.000 not 200. Here's the relevant pbs video

https://www.youtube.com/watch?v=EzZGPCyrpSU

And objects that have to carry their own fuel have problems even at much lower speeds.

It doesn't take the same amount of energy to accelerate (and later brake) to 0.5c as it does to accelerate to 0.1c.

0.1c would be sufficient for a single generation ship.

Depends on where you want to go. The universe is a pretty big place.