> 3. Even if you could go that fast, you'll eventually hit a speck of dust and disintegrate.
Can you elaborate on that? Do you mean if we clash with anything (even as small as a space dust) while traveling at a substantial fraction of c, it would disintegrate us?
It would cause damage. The faster you go, the worse is the damage. Even just the cosmic microwave background will eventually turn into dangerous gamma radiation, so you will need heavy lead shields in the front, which makes traveling even more expensive and difficult. At certain speeds, you should think of your spaceship as a drill penetrating the inter galactic medium. And even then the journey will take millions or billions of years (in the reference frame of those staying at home).
At 1% the speed of light (approx 3000000 m/s) and a medium-mass dust (1x10-5 kg, stationary), not enough force or area to dent steel (350 N/mm^2), but over time, lots of dust could cause erosion (quick math/estimates).
The relevant equation is for kinetic energy, which is 0.5mv^2. Using your numbers that's about 4.5E+7 Joules, or the energy of about 10kG of TNT exploding. That will certainly make a dent, and your space ship won't survive many of those.
I was thinking v would be more like 10% of c, which would mean about 1000kG (1 kiloton) of TNT, or about 1/20 of the energy of the Hiroshima atomic bomb. From a particle of dust weighing 10mG. You'd be toast.
Caveats:
1. It's really, really hard to supply enough energy to go that fast, even with fusion power.
2. Your passengers won't be able to go home again, because by the time they get back everyone they've ever known will be long dead.
3. Even if you could go that fast, you'll eventually hit a speck of dust and disintegrate.