Mathematically, a point on the edge of a surface is still a point on the surface. Just like if you ask for a number in the range 0 to 100, it's valid for me to give you 0 or 100 as they are still parts of that range.

And if not, I can still pick a point 0.00001 inches offset from one face, nothing says that it has to be the centre of one face. Also the cube can overlap with the space that you occupy, and can be oriented however you want.

Where it states that any creature (on a failed save) is pushed back 10 feet, does it matter what size the creature is? Just small and medium, or also larger or huge?

Thunderwave can expand very far and that is what makes it good

True

it seems week to be a 1st above level tho 

In my home games, I rule that the distance of which a creature is pushed increases by 10 feet for each spell slot above first, having it grow in tandem with the damage. It just makes more sense to me that way.

Honestly though, if you center it on yourself, you'd get hit by it too (RAW), though there wouldn't be any direction for you to be moved.
That's not the rules as intended (which is for the cube to be placed adjacent to your square), but I'd allow it at my table, even without the self damage. It's a fine spell, there's no reason to nerf the placement of the cube. 

They get pushed the full amount. Difficult terrain only affects your speed when you use a movement speed. 

How about if you're trying to hit enemies on all sides of the character casting the spell, have the character lay down and cast it above them.

The spell is not in fact centered on you, it is just originating from you meaning you need to be within one of the tiles (Or at it's corner/one side, uncertain.)

It Originates from you, as in the force pushing away is starting from your tile and pushing away, not originating at the center of the cube. 

Fus Roh Dah jokes aside, this spell is pretty decent.

The damage isn't anything impressive, and the range kinda sucks but what makes it better that burning hands is that it has the potential to move a group of enemies. In most open-field combat scenarios it's pretty useless, but in dungeon crawls it can really shine.

In alot of dungeon crawls when you open the door to a new room and see enemies, things will start to bunch up at the entry hall/doorway and it will be hard for people to position themselves where they need to be. This spell can push some things aside and help the melee users get into the room and be where they need to be. It's got some good battlefield control for tight spaces but is only really useful in cramped dungeons/chokepoints.

B-tier

FUS ROH DAH

Totally agree.  In my campaign we play this as a cone centered on the caster that effects targets in an area 15ft wide at 15ft out from the caster.  beginning of code is distance from caster's outstretched hands (so dependent on the caster's side.  

So, I'm trying to incorporate this spell as a racial trait for my homebrew character. Should I nerf this spell a bit? (Shorter range and power)

I know it says, "creatures", but it also damages fragile objects, surfaces, etc. that can take thunder damage, right?

I'm thinking of many interesting use cases in combat and narratively that coud becoming surprisingly complicated by collateral damage.

i would like to assume the cube is centered on you.

In my session we heard people behind a door. Our sorcerer used mage hand to open the door. Then our wizard used Thunderwave killing every goblin. Yet, we didn't see it because we closed the door and never checked that room again. GG ez.

druids cry

What if i throw some ball bearings and cast this spell in them? Would that be like the catapult spell? Is that like 3d8 x 1000?

Can anyone tell me the rules that are applied if an enemy (or player) is sent off a cliff by Thunderwave? I seem to recall reading that they should roll a saving throw to try and grab the edge of the cliff, but I can't find any information now.  Thanks