I’m making a plane heavy campaign and there will likely be many cases where planes will collide, or merge, or be created or destroyed. The same goes for demiplanes. How can we handle that? Are there rules or guidelines for handling these events?
There are no rules for planar collision.
D&D cosmology doesn't work like our universe. Some of the planes literally do not interact with one another. Even the planes that do interact could not collide/merge as you suggest.
There are cases where multiple material planes have collided/merged in the lore of previous editions, but this is different than other planes colliding/merging.
There are some rules regarding the incorporation of a demiplanes into one another. If you have a bag of holding (or similar item) inside of another, this happens:
Placing a bag of holding inside an extradimensional space created by a handy haversack, portable hole, or similar item instantly destroys both items and opens a gate to the Astral Plane.
So, seemingly if two demiplanes are incorporated (at least in this specific example), they annihilate and create a hole in the planar "barrier". It is unclear if a similar occurrence would take place with full planes.
Planes aren't like planets, they don't "crash into each other". However, parts of a plane might seep through a portal.
There is precedence for this event from the planes of Limbo or the Abyss.
The Githzerai, a psionics-focused people of monks that usually dwell in Limbo, sometimes teleport their fortresses, which are made of the highly unstable "limbonian" matter, to other planes. If they do so, the matter of the fortress causes harmful reactions with the target plane. Once the last Githzerai anarch (strong psionics master) leaves the plane, the fortress disappears.
See Mordenkainen's Tome of Foes, page 94/95 for further details.
Demons, on the other hand, only have to dwell in an area long enough until eventually a portal to the abyss opens automatically. Once this portal is open, demons will start using it to enter the target plane, spreading the seed of the abyss further. In the worst-case scenario, an entire plane can be turned into a layer of the abyss if its inhabitants don't defeat and push back the demons.
See Mordenkainen's Tome of Foes, page 24/25 for further details.
These are just two examples of two planes "colliding", although this doesn't happen the way planets would collide. You can base your own interpretation of planes interfering with each other on these examples, or come up with your own ideas - after all, your universe can always differ from the "official universe" as much as you like (although you should be careful not to shoot yourself in the knee with incoherences).
Do note by the way that, at least in earlier versions, there were multiple planets in the Forgotten Realms setting (and other settings; in fact, each setting was viewed as a separate "star system", so-to-speak). Type "D&D Realmspace" into a search engine of your choice for details.
5e, however, hasn't provided any material on the matter so far.