Hi

I know how planewalking works with Magic the Gathering, where the planewalkers draw their magic because I've done some research and resumed all of these in a document I've made a while back...  https://www.dropbox.com/sh/79zyh0fkaao5wgi/AABAPXx5ymAiyo9qEkQRGJW1a?dl=0 (page 108)

Now I'm wondering how it relates to DnD

Of course, any GM can create whatever story they want, whatever plane and planewalking dynamic that they want in their world...

What I want to know, is the known DnD world...whether it is games, books or described in the rulebook

1) How common is planewalking?

2) Is there any entities regulating planewalking?

3) Is there any form of on-going communication between agents in different world and such entities?

4) Is anyone planewalking for a living?

5) Where is a bag of holding sending the items?

6) Can you just kill people by putting them in your bag of holding? (Let say I rush a monster and drop a bag of holding on him...and then burn the bag?)

Thanks

 Now from my knowledge of DnD (limited but some) and MTG I would answer

1) No 2) Gods maybe 3) Gods to their worshiper but most likely not relating information between a plane to another 4) No 5) Compress the item or to the Aether 6) probably but that would suck

Now like I said, we can do whatever we want as a game creator, I'm not interested in that.  I'm told that there is existing ground in DnD for this, I want that proof...

There is a lot to unpack here...  So I am going to chime in on what I know on the official settings.   There are A LOT of prior to 5e material that has been written too, but the vast majority of it isn't "officially" updated to current.   So much is also setting specific and DM specific, so that NONE of the below is hard fast canon/rule of law.   

I am sure others are going to chime in here...but to start:

1. How Common is Planewalking?:  In the current 5e documented settings:
   1. Forgotten Realms:  Province of high level play generally, unless the story dictates other wise.  Places like Dragonspear Castle certainly have gates.
   2. Eberron:  Rarer than FR; most of Eberron is concerned with events after the last war.  The planes impact the worlds though, and sometimes the barriers are soft when they are coterminus, to Thelanis or Fernia based on the moon phases.  So travel is possible.  But it's story driven.
   3. Ravenica: I know the least about this setting from MTG.  So perhaps story wise you can educate me ;)
   4. DMG covered concepts:  Portals, Vortexes and gates exist.  The bones of the setting Planescape and Sigil are discussed, as are the other planes.  There is even a class (Ranger Horizon Walker) that can find portals.   But again, very story driven.

2. Is there any entities regulating planewalking?  Setting based mostly:

   1. Forgotten Realms: Any deity of travel I suppose is valid.  Certainly any being with Plane Shift is useful here for doing the travelling.  Many entities are interested in opening gates (See Princes of the Apocalypse or Out of the Abyss adventures).  But nothing really prevents it beyond the DM, and player power.  Nothing regulates it.
   2. Eberron:  Again, the moons of Eberron and if they are coterminous it can happen.  But no being is in charge per se.
   3. Ravenica:  Reading your own doc (page 108 or so) implies it happens, but I don't know the story line at all.
   4. DMG:  Only Sigil has anything like this;  The Lady of Pain of Sigil creates/shuts/opens portals at the DM's whim.  But you don't beg her for a portal, you beg someone else for knowledge and a key to open it.  You never ask the Lady for anything...unless you want to be mazed or flayed (and this is a bigger unpack on why, without a huge discussion of planescape and the setting.  I personally love it, but it isn't for everyone.

3. Is there any form of on-going communication between agents in different world and such entities?

1. Forgotten Realms:  Agents like Elminister and any other archmage or other high level casters could be.  But FR is focused on the matters at hand on Toril generally.  The planes intrude occasionally.  BUT again, this is a DM province on their story so...mileage will vary.
2. Eberron: Keith Baker the creator has a lot to say here; and generally the answer is no, with some exceptions.  Most planes like Fernia, or Risia are focused on themselves, and just aren't interested in the Prime.  Now, Dal Quor, and Xoriat are VERY interested in the prime for reasons.  Dal Quor has a lot of communication between agents in Sarlona and the Dreaming Dark...but that isn't exactly public commoners.  Xoriat and the Dalkyr are unknowable, and they invaded before.  But Xoriat is now remote and not contactable  Why?...well per Keith they are unknowable so its up to the DM, if they are using either set of bads as the story.
3. Ravenica:  I have no clue.
4. DMG:  Not as documented.  But folks that know of the Blood war between the Baatezu/Yugoloths/Tanar'ri (Devils/Daemons/Demons in common parlance) there is certainly some type of communication, as the war  does spill into the prime occasionally.  They need mortals to help the war effort...or at least their souls.  
4. Anyone planewalking for a living?
   1. Not really covered in any setting specifically.  Volo might...but I wouldn't call that safe transport.  Again, this was really the province of Planescape in general and that isn't a current setting.  Spelljammer is in a similar boat.  Both of those settings implied cross planar/sphere trade.  But the Primes generally had no clue that was going on.  
5. Where is a bag of holding sending the items
   1. Ohio.  Sorry...its not a plane or demi-plane, its extra dimensional space (page 153 of the DMG).  So its a magical mystery on how that works.  Quantum space?  Who knows.   Maybe Heward does.    
6. Can you just kill people by putting them in your bag of holding? (Let say I rush a monster and drop a bag of holding on him...and then burn the bag?)
   1. Well...you could destroy the bag sure.  DM's call I guess if all the items fall out or not.  Suffocation is implied.  But per sage advice they can open it from the inside unless it was sealed shut some how.  I would just firebolt the beasty and run around in a circle because I want my bag.

Regarding Bag of Holding:

It has it's own dimensional space a "pocket dimension". It's not a demiplane or plane but works similar: it's basically a very tiny mini-verse that has up to 64 cubic feet (equivalent to a 4 ft cube) of space in volume. If you're putting a creature in there it has to be pretty small. The space has no oxygen beyond what it keeps from when it is opened which is about 10 minutes of air which is divided between the creatures inside (1 creature gets 10 minutes of air, whereas 10 creatures would get 1 minute of air). When those minutes run out they can no longer breathe and will suffocate.

Nothing stops a creature opening the bag from the inside. Creatures with planar travel can also escape that way. A creature can use an action to open the bag from the inside. If you prevent it from being opened and the creature does not have planar travel it can escape by damaging the inside. Any tear, hole or anything destroys the bag sending all contents to the Astral Plane. The Astral Plane allows you to find a portal to a plane of your choice within mere hours and is considered reasonably safe and more reliable way to travel through planes (gods and deities can ward against or shut down portals and plane shifts, but cannot block the naturally occuring portals the astral plane uses). So, very good chance the creature can easily and safely escape albeit in an inconvenient way. This also occurs if you damage the bag from the outside.