I know it is possible that a star system ejects a planet out of the star system and the planets becomes rogue planets and orbit around the galaxy. Is it also possible that a planet gains enough speed because of ejecting and escapes out of the galaxy?
Intergalactic planets have never been observed. They're too small and it's too great a distance, but intergalactic stars have, and if stars can be ejected from a galaxy, planets can to. The orbital mechanics is the same for both.
The escape velocity of the galaxy is impressive. For solar-systems, where most of the mass is in the star in the center, the escape velocity is just about the orbital velocity times the square root of two. Source.
For the Milky way excape velocity calculation is larger and more complicated because most of the mass is in the dark matter halo and very much spread out, not localized in the center. The center is still more dense, the mass is far more distributed so the square root of two rule doesn't apply. Using the Sun as an example, the orbital velocity of our sun is about 220 km/s and it's escape velocity is 537 km/s. Source. As objects moves further towards the edge of the Milky way, the escape velocity decreases and the orbital velocity generally increases, so at close to the edge of the Milky way, you'd get something close to the square root of two ratio again. That means an object close to the edge of the Milky way only needs to add 41.4% of it's velocity to escape.
Gravity assists depend on the relative velocity of the larger object to the "stationary Milkyway", so, if our solar-system was to fly close enough to very massive star and get a big gravity assist, assuming the massive star has a similar orbital velocity around the Milky way, 220 km/s, that could add as much as 440 km/s to our solar-system's velocity which would be enough to escape the Milky way. Only large stars have enough gravity for that kind of kick, but there's enough large stars in our galaxy that they shouldn't have a hard time ejecting objects that fly reasonably close to them. You probably need at least a half dozen or dozen or so solar masses and a close fly-by, but, statistically, it should happen from time to time.
The Wikipedia article points out that galactic collisions could be responsible for these stellar ejections, and galactic collisions probably do eject a great deal more material compared to a galaxy in a peaceful spiral arm rotation, but it's still possible for gravity assists to cause objects to be ejected even from a galaxy not currently colliding with anohter, because twice the orbital velocity of the large star plus the orbital velocity of the approaching star or planet, when combined is greater than escape velocity, at least for the outer parts of the spiral galaxy. Needless to say, most gravity assists don't line up perfectly, and half of them push an object further in, not further out, but statistically, and with multiple assists, it's very likely that stars and rogue planets get ejected from the Milky-way, it's probably happening as I write this.
By some estimates, there might be a HUGE number of objects that doesn't belong to any galaxy.
To my understanding, yes. This is not to say that eventually it may return to its original host galaxy over billions of years.
I would think the frequency of such events would be higher during galaxy mergers/collisions.
I recall a report of an ejected supermassive black hole identified that had been ejected from its host galaxy.
I'd like to point out another interesting side of this question. You specifically ask
Is it also possible that a planet gains enough speed because of ejecting and escapes out of the galaxy?
This question doesn't specify the means of ejecting which opens the possibilities for interesting results. The normal process of ejection, causing rogue planets, is a gravitational collision (note the difference from physical collision) between two planets in a given stellar system, usually during the formation period. The ejection speed of the ejected planet relies on the mass of the two "colliding" planets.
While it varies widely depending on where you are in the galaxy, the escape velocity from our rough position in the galaxy can be calculated to be $\sim500\:km/s$. This is really fast and more than double our orbital speed around the galaxy. Planetary collisions are highly unlikely to cause such an ejection speed.
So if two colliding planets in a stellar system can't cause one to be ejected outside our galaxy, how might it happen? The answer is stellar collisions. If the ejected speed relies on mass, throw some more mass in there. We have observed numerous examples of what we call Hypervelocity Stars. These are stars moving throughout our galaxy at velocities on the order of $\sim1000\:km/s$ or more and are thus on an escape trajectory.
It is not completely known exactly how these stars achieve such a monstrous velocity, but they seem to originate from dense stellar regions such as the core of the galaxy or stellar clusters. This implies the cause is from chance stellar collisions where one star just so happens to get a huge velocity boost.
If this can happen to stars, why not planets? It would likely be a very rare occurrence, but I can imagine a scenario where a planet forms around a star in one of these dense regions, that star gravitationally interacts with another star and with the proper setup, the planet is ejected at high speeds in the process.