Based on the first assumption:
- The impacting planet orbited the star at roughly the same speed as the other planet
This means that the impacting planet is in the same orbit as our inhabited planet, since speed and orbit are much the same thing.
Obviously this isn't a stable arrangement, but it's more stable than it seems on the face of it, because as an object picks up speed, its orbit gets longer, and as its orbit gets longer, the time it takes to orbit increases.
- Something (asteroid strike?) has caused the orbit of the impacting planet to degrade such that it is spiraling in towards the star
Orbits don't spiral, unless you have some constant source of energy slowing the object down. Satellites spiral down because the atmosphere produces drag. This couldn't be the case with another planet. In fact, our moon is being accelerated into a higher orbit away from Earth. Unless the other planet were well inside of the Moon's orbit, close enough to already be doing widespread damage just by interacting with our atmosphere and heating it up, there is no way for the other planet to spiral down to our inhabited planet.
- The angle of impact will be acute, as one planet effectively "merges" into the other planet's spot
The angle will actually be face-on, if our first assumption is true. I'll get to that in a bit.
- Speed of impact will be slow
Again, not if the first assumption is true.
Really it comes down to whether the uninhabited planet's orbit suddenly became very elliptical (that is, if Mars's orbit suddenly changed so that its closest point to the Sun is within Earth's normal orbit, but its furthest point is still at its original orbit), or whether we have two bodies that have been sharing the same orbit around their star and are about to meet their inevitable ends.
WhatRoughBeast has already provided an excellent answer in case it's a Hoffman Transfer orbit (including the fact that Mindwin's answer is spectacularly wrong), so for that scenario, I'll only repeat the most important detail, that the speed of impact will be 9.5 km/sec, and I only repeat it in case WhatRoughBeast's answer somehow goes missing.
I'll also add, since it's asked in the question but I haven't seen a good explanation in any other answers yet:
From the point of view of someone on the surface, but far enough over the horizon to not see the impact, your first and only warning will be an earthquake that gets stronger very quickly, over the course of a few seconds, until the ground is shaking too violently for you to stay on its surface... You will be thrown about like a ragdoll, each impact more violent than the last, until you sustain sufficient brain injury or spinal cord injury that you lose consciousness... Once the rumbling starts, you'll probably have 20 seconds of consciousness. You'll be too busy being thrown around to notice that the ground is heating up from all of the friction, and within 5 minutes, the ambient heat will be enough to cause any carbon based life forms to spontaneously combust.
From the point of view of someone who can see the impact: Things get hot very quickly. You might have a second of consciousness if you're behind a mountain.
Now, on to the meat of my answer:
If the two planets are traveling at the same speed (first assumption from the question), they'll be in the same orbit.
Orbits are tricky, though. As you gain more speed, the size of your orbit increases... The bigger your orbit, the longer it takes you to complete that orbit. Thus, if you want to slow down compared to another body in the same orbit, you pick up speed. (That is, you go further away from your star, and just as Venus orbits the Sun more often per Earth year than Mars does, you'll be orbiting your star less often.)
Now, with two rocky planets, there's a lot of gravity, which means that as they get closer, there's a lot of acceleration. They will both attract each other, and if they're both the same size, they'll attract each other equally.
The planet in front will slow down, and the one behind will speed up.
But since we're orbiting, any slowing down and speeding up will affect the size of our orbits. The planet in front will get closer to its star, and the planet chasing will get further away.
The first time this happens, someone on the surface will see an incredibly bright planet. Brighter than Venus or even the International Space Station, and you might even be able to make out its illuminated side (it'll look like a half circle). Assuming our inhabited planet is the ahead planet, the chasing planet will be visible from dusk to midnight.
The orbits of both planets then get more elongated, but only astronomers and people who keep track of time would notice at first.
After a couple of years, things are reversed... Our inhabited planet has sped away from the chasing planet, and is now doing the chasing. As it approaches the rogue planet, it becomes visible in the morning sky, from midnight to dawn (and even visible during the day, if you know where to look, until noon). Our inhabited planet gains speed, the rogue planet loses speed, they get a few million miles closer than they did before, and miss each other by a large margin once again... this time, with our inhabited planet in a larger orbit and our rogue planet in a smaller orbit zipping away.
This cycle repeats for a couple centuries (a mere blink of an eye in astronomical terms... the Earth is 4.5 billion years old; this is 1/20,000,000th the time frame... There are comets that visit the sun once every million years). Now things get interesting.
Towards the end of the cycle, there are no moons around these planets, if there ever were any. The gravity battle has pulled all satellites away, natural or artificial. The fourth to last orbit, the rogue planet gets to within 1/5th the distance of the Earth to the Moon. (For scale, imagine a typical classroom. If the Earth is the size of a basketball, the Moon is a grapefruit... and both would be in opposite corners of the room.) There would be earthquakes and volcanoes during the weeks that the two planets are closest to each other... During the month leading up to the encounter, the rogue planet is hidden by the glare of the star, but after the encounter, it dominates the night sky well past midnight. Careful observations would be able to see the rogue planet moving across the background stars during the evening of closest approach.
9 months later, things are considerably closer, earthquakes are larger, and the timing is reversed... The month leading up to the encounter, the rogue hangs heavy in the night sky, and after the encounter disappears into the glare of the star.
9 months later, greater earthquakes damage every standing building, destroying most... the planet passes within 20,000 miles of ours, appearing out of the sun's glare, and absolutely dominating the night sky, their relative speeds are so great and both bodies are so close that you can see the other planet spinning above you.
9 months again, the rogue planet comes... The night before it passes, it starts to enter your planet's penumbra (out of focus shadow... an area experiencing a partial eclipse), then slowly creeps into the umbra (full shadow, are experiencing a total eclipse).
The two planets will collide with all of the force of a head-on collision, about 60km/s.
Anyone who can see the impact will die immediately. The atoms of their bodies will be stripped apart faster than the neurons carrying the information about what's going on could process that data. If they're close enough to "see" the flash, their brains will never experience the sensation.
There won't be a low rumble that will turn into an earthquake that will throw people against other objects to their deaths, like in a "slow" 9km/s impact... There will be one shockwave that moves at supersonic speed through the mantle of the planet, and as soon as the ground beneath your feet experiences that shockwave, the ground will be moving so fast that you'll just go splat.
Planetary collisions are nature's way of asking how that space program is coming along...