Gravity effects with mass make no sense

So we have this ENORMOUS ship (as proven by the beginning of the movie) going way faster than light speed, accelerating all the way to 'ludicrous speed' (however many AU per second that may be).

Why does the spacecraft have gravity, but yet accelerates as if it has no mass? I mean, why does a fast speed make Dark Helmet fly sideways and crash into the contro panel when they stop? You don't get that kind of effect due to SPEED, only due to ACCELERATION/DECELERATION.

However, NO self-respecting spacefaring people would ever make a spacecraft where you can actually feel the effects of acceleration/deceleration at THOSE SPEEDS, because it would be physically impossible, but even if it was physically possible, it would CRUSH YOU TO DUST because the acceleration is.. let's say 'SLIGHTLY' stronger than with a car on this planet (even Tesla).

Furthermore, as we all know, approaching light speed WITHOUT doing something about the mass property or at least generating a protective energy field around the craft and elevating the vibration frequency of that field (or even the hull, which is more dangerous due to the unpredictable changes in structure it may cause), would just INCREASE the mass of everything inside the ship so much that if they're subject to THAT kind of acceleration forces, .. need I continue? It just wouldn't work in either case, and Dark Helmet would be crushed to little particles for more reasons than one.

There would be incredibly powerful forces tearing everything apart if they retain the mass property while accelerating that fast into that kind of speed (which wouldn't even be physically possible, which is why many still foolishly and blindly believe achieving light speed is impossible (though light already did it), because they can't understand that it's only impossible purely on the physical side).

In any case, Dark Helmet flying into the control panel makes NO sense unless they're just in some amusement park ride instead of a friggin' spaceship going friggin' faster than light.

Also, there's NO WAY that kind of mass, retaining its mass property, can just ACCELERATE that fast - we're shown two contradictory things: a) How MASSIVELY ENORMOUS the ship is (and thus incalculable mass) b) How FAST it accelerates to light speed and beyond (not possible without removing the mass property or elevating the vibration frequency around the ship or the hull of the ship, or the whole ship, which would be incredibly dangerous, of course - the first option is the safest).

So none of these 'gravity effects' make any sense unless they do something about the 'mass' problem, but they couldn't even create localized gravity that is independend on the acceleration/deceleration, so nothing about it makes any sense.