RAW, they will not awaken.
The sleep spell clearly lists the ways to awaken the sleeper. This is magical slumber, which can occur even in the pitch of mortal combat (in fact usually in the pitch of mortal combat). It is not ordinary sleep. Note that the action to awaken the sleeper is to take damage, or be shaken or slapped. The spell says nothing about loud noises, bright lights or other things that normally awaken sleepers.
The entangle spell has no language in it that describes a level of violence even so mild as a slap or shake. A DM is free to interpret this otherwise (that's their job), but there is no specific language in the rules to suggest that the entangle spell will awaken a magically slept person.
RAW is unclear, but likely not
Neither square or hover are clearly defined terms but from their context we can draw decent conclusions.
A hovering creature is still flying and would not be within the 2-D area of effect for entangle.
Entangle's Area of Effect
The area of effect for entangle is a 20-foot square. Square is not one of the shapes listed in the PHB section on areas of effect (PHB, p. 204). The DMG only mentions it as "Cube or Square" when determining the number of creatures within an area for gridless play (DMG, p. 249). Additionally, both the PHB and the DMG are fairly light on 3-dimensional rules like height for things other than cubes, spheres and cylinders.
In contrast the spell web has an area of effect of a 20-foot cube when anchored. Without anchors its area is describe as:
Webs layered over a flat surface have a depth of 5 feet.
We don't have a rule for how high the area of effect for entangle reaches, and therefore how high the demilich would need to be to avoid it.
In my interpretation, square is a 2-dimensional version of cube, therefore it has no height and a creature must be on the ground in the area to be effected. Therefore unless the demilich is touching the ground (which it doesn't need to) it should not be affected.
Hover ability
From the Flying Movement section under Movement and Position (PHB, p. 191) we have the meaning of "hover" (emphasis mine):
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover [...]
The demilich's hover ability prevents it from falling when knocked prone, but otherwise has no effect on area of effect for spells like entangle. It does mean that the demilich can choose to be at any height without fear of touching the ground; however, other than that, it obeys the regular rules for flight.
To clear up confusion, hover is a more powerful version of flight, not less. Would you rule that a creature flying 5ft above the ground is effected by entangle? I would rule that it is not. So a hovering creature would not be effected either.
Best Answer
No, generally a wall is not the same as the ground
The rules do not define what the word ground means, which means we use the common English definition:
Thus, according to the rules as written and common English definition, a traditional manufactured wall is clearly not ground.
As Jeremy Crawford has said:
Which leads me to my next point...
...But many cases may come down to a DM ruling
However, there are definitely edge cases here. For example when you are falling down a pit dug into the earth. Or alongside a cliff face. However, these are edge cases that the DM must decide since they can go either way and the rules are vague.
If your DM is willing to accept an even more lenient view of what ground is, they could even extend the definition to include things like walls and structures. However, this would be a houserule at your table. It also has the potential downside of making the spell potentially a lot more versatile than the designers intended. After all, if walls could count as ground potentially any solid surface could. If your DM is fine with this though, it is within their power to rule it as such.
As Jeremy Crawford has also said:
It is important to note that there are other spells that also must be cast on the ground so a DM should consider carefully before allowing it for all.