On top of that, warp and impulse are related, but, as a character in one of the better novels put it, "warp is as far above impulse as impulse is above walking". Both are distortion drives, but the order of magnitude difference is vast. Note here: This is also one of the things I've talked with Rick Sternbach about after his active involvement with Trek ended, and what I talk about here is what Gene, Matt Jeffries, the RAND Corporation, and a few others associated with TOS through about TMP operated from. And that I can, for the most part, rationalize into TNG-Voyager Trek.
Basically, imagine impulse as a big gyroscope. Have you ever done one of those things a lot of science museums have? The bicycle wheel you hold and stand on the well-lubricated turntable? You hold the wheel vertical while it's spinning, you're stationary. Tilt it one way, you start turning the opposite direction, and vice versa. Impulse and Trek's artificial gravity are, basically, space/time/gravity versions of that. Look at the back end of the 1990s-vintage
Botany Bay, one of an unknown number of DY-100 cargo haulers, an unknown number of which were used as sleeper ships (Think they's waste that tech sending Khan and his followers into exile if it was the only extant example? They'd've just executed them or marooned them on Mars or something.):
Not a lot that can be used for potential "thrust exhausts". In the later era, Greg Jein and Mike Okuda did art and models from the conceit this ship was launched from Earth with a booster cluster, when the original designer intended it to have been built in a "space drydock" and, like the TOS
Enterprise, was meant to never enter atmosphere, coming or going. This was the era of great space optimism, that we also saw in the middle act of 2001 -- five big space stations at the LaGrange Points, permanent bases dug into the moon, manned expeditions to Mars and the outer planets -- all by the year 2000. That ship was intended to go from space station to space station in an era we were expecting in the 1960, were seeing by the mid-1970s was unlikely, and that we ended up never getting. Star Trek's future history is and should always be derived from that.
Notice also the impulse engines in TOS were always dark. Those rectangular holes (on the versions of the impulse deck that even
had holes) weren't thrust exhausts. Most likely, just creating better exposure to heat-exchangers. Much like the TOS Bird of Prey, early human ships -- slower than light and faster -- were powered by "simple impulse". Fusion-powered distortion drive systems. By TMP, with the new, higher-energy-producing intermix reactor assembly, matter-antimatter-derived warp plasma ran everything, from phasers to impulse engines. Hence the big impulse deflection crystal at the top of the vertical intermix assembly. So now the heat-exchangers are right out there, and glowing orange-yellow when the drive is engaged.
Romulans and Vulcans have had FTL drives for a while. Since easily hundreds of years before us. But notice the "works-just fine-thanks" version the Vulcans used from pre-TOS all the way up -- the "ringship" design. That's basically a giant impulse coil rotated 90° to the direction of primary travel, and then stacked with others. Fired in sequence, the distortion effect is stronger and warps space/time past the ship faster than the apparent speed of light -- even though the ship is moving, within its own internal frame of reference, just as fast as it was before the warp was engaged... If it was moving at all. A ship can go from dead relative stop to warp, and then once the warp field dissipates, they'd have the same inertia as they did before -- dead stop. Cochrane's big breakthrough was realizing this (before the Vulcans made First Contact) and, rather than making a big coil stack on the ship's centerline, he made smaller coils and mounted them in a pair of offset engines. By throttling the plasma flow to one or the other, you can "steer", like dragging an oar. That both impulse and warp are non-Newtonian drive systems is something a lot of people don't get.
Now, as for why they don't hit anything... For some time everyone was limited to low-warp in our neck of the woods. Or, more specifically, warp jumps. You scan out as far as you can to make sure your path is free of significant obstacles, warp out to the edge of that range, stop, do another scan, etc. Limits the effective range of colonization and commerce. Had to wait until FTL-boosted computers and sensors came along. That then created the demand for faster ships, etc. The main long-range sensor is still oriented along the flight path, because that's where you need to be able to see the furthest, so as to not have already hit something by the time you see it. That parabolic dish also generates a set of "nested-bubble" passive deflector fields that catch subatomic particles, ionized gas and other interstellar media and shunt them out of the flight path. For larger objects, there are the active deflector beams that are projected way out ahead to move aside meteoroids and other macro-scale objects. If it's bigger than a certain size, the ship just tweaks its course around the object -- originally manually, later automatically but with organic redundancy (a conn officer monitoring the forward sweeps). On the TOS and TMP
Enterprise, the deflector emitters are those three boxy structures flanking the main sensor dish. On the
Excelsior, they're the two greeblied inserts in the ship's neck, above the dish. From the
Ambassador class on, a few things changed.
The active deflectors are incorporated into the main long-range sensor, which also has more range and sensitivity, the computers are faster and can cope with more sensor data at high speed. And the impulse engines now have their own "warp coils" to lower the ship's inertial mass so smaller impulse engines can push a big ship. I love the
Voyager for basically being the ultimate expression of what Gene was going for with the
Enterprise-D -- refinement, amplification, miniaturization. Andy Probert designed the TNG
Enterprise with smaller engines for the vessel's size than the original at Gene's behest to show this progress (even though Gene later had him add a little bit back on to the engines' back ends). I only wish Rick's vision of
Voyager's engines was practicable at the time -- partly for maximum warp field efficiency and partly to mitigate the erosive effect of warp fields on the subspace-realspace "barrier", the engines were supposed to move in flight. Lower for lower warp, higher for higher warp, shifting slightly at warp to adjust for local variation in field strength, etc. And, frankly, I wish they only ever went full horizontal when the ship was landing. Woulda been a nice surprise to keep for further into the show.
A bit of an essay, I know, but you have to know
how the drive system works before you can address how it interacts with physical objects around the ship.