Acceleration in Galaxies Collision In the far future the Milky Way and Andromeda will collide.
As far I know direct collision between large dense objects (black holes, stars, planets, etc.) is unlikely due to the relative "low density" of both galaxies.
My naive intuition is it's like two big clouds of dust merging.

I know at the collision time the Sun will be most like a red star and Earth a scorched dead planet.
For the sake of the next questions let's hypothesise another system with a star resembling the Sun and another small beautiful third rocky blue planet holding some advanced live form.
Also, for acceleration measures, let's use a frame of reference like if someone is observing from far away both galaxies getting close one to another and interacting.

Some questions pop up in my mind.


Can the gravitational interaction sling shot an entire stellar system? How much Km/s2 we can expect these system to accelerate? (In a most extreme plausible case).
How this acceleration can affect the system? Can it de-stabilise planet orbits for example?
How it can affect life? Can it affect magnetosphere? change it's shape? Can solar flares/wind get stronger in some path due particles acceleration?
If another star passes really near (let's say 1 light year at closest approach) but at great speed can its light reach that planet at high energy levels, let's say x-ray and affect that planet life?
The short answer is no. There is no huge accelerations of star systems. 

Look at a pair of interacting galaxies  These are the Antenna galaxies (image copyright Star Shadows Remote Observatory and PROMPT/CTIO, from apod)

You will see the long "antennae", which are formed of stars which have been ejected from their galaxies by the interaction. But the accelerations needed are not large, because the interaction takes a long time. The acceleration nothing like $km/s^2$, The force required to accelerate a planet like that would smash it. remember 1$km/s^2$ is about 100g. But small accelerations over long periods can have big effects. The only way to cause objects to accelerate is to apply a force, and the only force that can move planets is gravity. A galaxy has a great big gravitational field, but it is very spread out, and as you note, most of the galaxy is empty space.

Planet orbits should be stable, certainly inner planets would remain bound to their stars. There could be disruption to oort clouds, but the gravitational field around a star would not change much. Similarly the star's magnetosphere would not be changed much. As above there are no large forces applied to stars or planets.

A close-ish approach, to 1 light year, would cause disruption of the oort cloud, but nothing more. Stars may have larger relative motions, but no where near enough to cause blue shifting of light into x-ray, in fact it would be hard for observers on the planet to tell which stars came from which galaxy. Andromeda is approching at 120km/s. But proper motions of stars in the milkyway can be greater than this, Barnards star has a relative velocity of 142km/s

At the end of the interaction, the star and its planet is likely to be scattered to the halo of an elliptical galaxy.