Compared to the effects an impact of a global killer would have on Earth, what if such an asteroid, with a diameter around 7 miles (11.2 km), impacted the red planet with its different atmosphere, size and gravity? Would any volcanoes erupt? And what effects would such impact have on the probes and rovers currently on Mars and on its exploration?
Imagine a similar asteroid as Chicxulub, the one that likely killed the dinosaurs here on earth. It is thought to have impacted at about 20 km/s.
Initial atmospheric effects: When the asteroid entered the Earth's atmosphere, it pressurized the atmosphere and caused faster than 1000 km/hr super-heated winds - https://www.lpi.usra.edu/science/kring/Chicxulub/regional-effects/ that blasted out in a 1500km radius. Since Mars's atmosphere at the surface is less than 1% the density of earth's, the heat generated by pressurization would have been correspondingly at 1% given the ideal gas law tells us that heat and pressure have an inverse relationship. The super-heated winds, glowing heat release on atmo-entry, and asteroid ablation would be disappointing on Mars compared to Earth.
Impact and initial ejecta: On Earth, the Chixculub impactor hit in the shallow ocean near the Yucatan, causing a huge tsunami that covered most of what is now the South East United States. The water landing softened the blow, but enough energy was released to vaporize the meteor and blow out enormous amounts of ejecta. The big ejecta (a few centimeters to 300 meters in diameter and bigger) landed hundreds of kilometers away in just a few minutes. Much of the smaller ejecta floated down thousands of kilometers away. A convection reaction dust plume at the impact site pumped soot and dust into the upper atmosphere and beyond. This ejecta (which was mostly vapor) sped up as it rose. As much as 12% of this ejecta reached escape velocity and never came back down to earth! https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2001JE001532
On Mars, there wouldn't be any tsunamis of course, since there is no ocean. Hence the impact would kick up more debris. Since Mars's surface gravity is about 3/8 of Earth's, and since there is much less atmospheric resistance for objects moving in the atmosphere, the big ejecta would have traveled thousands of kilometers instead of hundreds. A lot of this ejecta (especially the vapors and liquids) would have gone into orbit or reached escape velocity! However, the convection dust plume at the impact site would have been smaller than on Earth, with less atmosphere to feed the plume.
Debris layering: Since the area of a sphere is $4\pi r^2$ and the radius of Mars isn't much larger than half that of Earth, we can estimate that the surface area of Mars isn't much more than 1/4th that of Earth. So the debris layer would be almost 4 times thicker (really much more because there would be more debris in an impact with no water). On Mars, the debris would be centimeters to meters thick (nearer the impact site) rather than on Earth, were it is only mm thick opposite the impact strike. Also, due to the lower atmospheric density, particles would settle out much more rapidly than the decades long global cooling Earth experienced.
Volcanism and Earthquakes: I agree with the other answer, an asteroid strike of this magnitude likely caused volcanism on Earth and would likely do so on Mars. This would be to a lesser extent since Mars has a thicker crust, is cooler, and has less current volcanic activity. The Chicxulub strike was thought to be equivalent to an earthquake of magnitude 10 on the Richter scale. Enormous shockwaves would move across the entire planet and meet at the antipodal point, likely causing eruptions or even raising hills or mountains.
Rovers and Probes: The big effect an asteroid strike like this would have on rovers and probes is to destroy them if they were near the impact site, damage them with earthquake effects if they were somewhat distant, and envelope them with debris wherever they were on the planet's surface!
A partial answer to this part:
Would any volcanoes erupt?
At a local scale (i.e., close to the impact), such an asteroid could melt the rock, see impactite. But this not really volcanism as in sustained outpouring of magma from the interior of the planet.
However, there is a theory that large asteroid impacts could trigger hotspot volcanism at the antipodal point, where the seismic energy focuses. On Earth, it has been suggested that the Chicxulub impact could have triggered the eruption of the antipodal (and synchronous) Deccan Traps (Richards et al., 2015). On Mars, the same process has been suggested (Williams & Greeley, 1994): Alba Mons, the largest volcano of the planet, is antipodal to Hellas Planitia, the largest impact structure.