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. 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 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.
There are no rules for this, but you can take guidance from AD&D 2e and/or D&D 3e.
There is an interesting section on The Inner Planes in the Dungeon Master Guide revised edition of AD&D 2e:
The Inner Planes
Using the sphere analogy, outside of the Primes and the Ethereal planes are the inner planes, the primary building forces of the multiverse. The inner planes consist of the elemental, para-elemental, and quasi-elemental planes, and the planes of energy. The elemental planes are the building blocks of matter—Air, Water, Fire, and Earth. Where the elemental planes touch each other there arise the para-elemental planes—Smoke, Ice, Ooze, and Magma. The Energy planes are the Positive Energy plane (also called the Plane of Life) and the Negative Energy plane (the source of entropy). The quasi-elemental planes exist where the elemental planes touch the Energy planes—Lightning, Steam, Minerals, and Radiance around the Positive Energy plane, and Salt, Vacuum, Ash, and Dust around the Negative Energy plane. Many of the planes have their own creatures and rulers who are sometimes summoned to one of the primes through spells or magical items.
In the 3e you can look at Manual of the Planes (MoTP) which has extenstive discussion on the borders of planes. There is a section Chapter 6 on the Inner Planes which may be helfpul:
These border regions work if the borders between the Inner Planes are indistinct and gradual, with one element slowly giving way to another. There are other approaches that work just as well.
Set Borders: The planes have hard edges. A cliff marks where the Elemental Plane of Earth ends, and a wall of water marks the boundary of the Elemental Plane of Water.
Shifting Borders: The planes have edges that move back and forth, creating regions that share the traits of both Inner Planes, but only one set of traits applies at a time. Imagine a scarred landscape wracked by volcanic eruptions and lava flows when it lies on the Elemental Plane of Fire, and constant earthquakes when it lies on the Elemental Plane of Earth.
Elemental Pockets: Regions of one plane erupt onto another plane. If a pocket of the Elemental Plane of Earth emerges onto the Elemental Plane of Fire, the earth suffers all the normal effects for being there, but a vortex to the Elemental Plane of Earth exists at the heart of the outgrowth. Such elemental pockets usually have a guardian from the original Elemental Plane or Energy Plane at the vortex.
(MoTP p. 66)
Since there is no published material yet for 5e, you can use these as examples to base your campaign's Cosomology. As a DM you decide the size and borders of each plane of existence and if you with to have a plane "collide" with another, so be it.
...and always carry a scroll with Enhance Ability and Guidance and procure an Amulet of the Planes. Just in case.
I think that if, for example, the plane of air and the material plane collided, portals would open, gravity would become more of a guideline than a law, and winds would become stronger. Towards the planes of ice and ash, the air might become hotter and dryer, and ash might rain from the sky, or glaciers would pop into existence, the air becoming freezing and wet.