The exact rules of resting are left vague, as it says in the link you included. The exact method of resting is generally up to the dungeon master, but in general you can expect that to rest you need only be able to spend the full length of time, 8 hours for example, sleeping in a location where you will not be interrupted. It is not stated anywhere that you need a bed, or something similar, but the DM may say otherwise.

As for having to wait in real life, no you do not have to wait. Generally the DM will just say that you have rested and do a time skip, or say that you have been interrupted by a wandering monster which would require an encounter, for example, and then continue play.

There's nothing that special about the ability earth glide. Really. It's not the ability to become, like, totally intangible to earth or anything. At its core, it's just better burrowing. But I can sense your frustration; let me assuage it a bit by saying

The Various Earth Glide Abilities Aren't That Different

Perhaps it's helpful to see them in a list.

1. The monstrous extraordinary ability earth glide reads

   When the creature burrows, it can pass through stone, dirt, or almost any other sort of earth except metal as easily as a fish swims through water. If protected against fire damage, it can even glide through lava. Its burrowing leaves behind no tunnel or hole, nor does it create any ripple or other sign of its presence. A move earth spell cast on an area containing the burrowing creature flings it back 30 feet, stunning it for 1 round unless it succeeds on a DC 15 Fortitude save.

   There is no substantial difference between the earth elemental's extraordinary ability earth glide and the monstrous special ability earth glide.

2. The description of the spell earth glide reads

   The target can pass through stone, dirt, or almost any other sort of earth except metal as easily as a fish swims through water, traveling at a speed of 5 feet. If protected against fire damage, it can move through lava. This movement leaves behind no tunnel or hole, nor does it create any ripple or other sign of its presence. It requires as much concentration as walking, so the subject can attack or cast spells normally, but cannot charge or run. Casting move earth on an area containing the target flings the target back 30 feet, stunning it for 1 round (DC 15 Fort negates). This spell does not give the target the ability to breathe underground, so when passing through solid material, the creature must hold its breath.

3. The deep earth sorcerous bloodline reads

   Earth Glide (Ex): At 15th level, you can glide through any sort of natural earth or stone as easily as a fish swims through water, with a burrow speed equal to half your normal speed. You do not leave a tunnel or trace of your passage. You can use this ability for 1 minute per sorcerer level each day. The duration need not be continuous, but it must be used in 1-minute increments.

4. The odd one out is the earth wizard school which reads

   Earth Glide (Su): At 8th level, you gain the ability to move through earth, dirt, and stone for a number of rounds per day equal to your wizard level. You cannot move through worked earth or stone; only natural substances can be traversed. If your total duration expires before you exit the earth, you are flung back to the point where you entered the stone, take 4d6 points of damage, and are stunned for 1 round. Your burrowing does not leave a hole, nor does it give any sign of your presence (although you can be detected by creatures with tremorsense). These rounds do not need to be consecutive.

Summary

• Without a burrow speed a creature can't use the ability earth glide. 1 assumes the creature has a burrow speed. 2 essentially grants the caster a 5 ft. burrow speed so that the creature can use the ability earth glide. 3's burrow speed is half its "normal" speed, a term subject to some debate but one on which the table should quickly reach consensus. 4 requires a house rule--it makes sense to base the creature's burrow speed on that of a creature with the deep earth sorcerer bloodline (i.e. half the creature's "normal" speed). (Unless, of course, the DM believes the creature who takes such a school should already have a burrow speed--a not unreasonable but nonetheless unusual expectation.)

• The ability earth glide grants no additional senses nor the ability to survive while submerged. A creature who's using the ability earth glide gains no ability to navigate while doing so via the ability earth glide; the extraordinary ability tremorsense is recommended to do so. The DM may rule a creature without the ability to navigate is effectively blind when using the ability earth glide. Further, a creature who is using the ability earth glide risks suffocation; the ability earth glide grants no method of survival while using the ability.

• Can a creature do X while using the ability earth glide? The answer to every question wondering about X requires asking another question: Could the creature do X while walking? If the answer is Yes, then the creature can do X while using the ability earth glide. If the answer is No, then the creature can't do X while using the ability earth glide. The ability earth glide modifies to the way the creature's burrow speed functions, which otherwise follows the rules of movement.

  Alternately, the question that may need asking is Could the creature do X while in his space yet surrounded on all sides by impassable barriers? While not moving, the creature isn't using the ability earth glide, and the ability earth glide has no effect.

• For the creature how permeable is the material through which a creature can use the ability earth glide? This is unanswered by any of the ability's descriptions. Without further clarification, the DM must determine if the materials are equivalent to air, water, thick mud, or whatever. Also, the DM must determine--if he determines the material is thicker than air--what effect a spell like freedom of movement will have on the creature's capacity to employ the ability earth glide.

• The sorcerer and wizard abilities earth glide only function through natural materials. The DM must define what's natural for the setting. This isn't weird, but it is arbitrary. It's part of a hoary tradition to allow DMs to say No to an ability that has the potential to be abused. Unnatural material might be walls of stone for one DM, while an unusual ore from the Elemental Plane of Earth would be another DM's unnatural stone.

Specific Questions

• Can a creature be partially submerged while using the ability earth glide? Ask the DM. I'd say Yes and use the Aquatic Terrain rules for Attacking on Land.
• Must a creature be moving to use the ability earth glide? Yes. When the creature stops moving, the creature's not burrowing and therefore the ability earth glide has no effect.
• Does a creature with the ability earth glide threaten squares outside of the area into which he's submerged? No. the creature's not burrowing and therefore the ability earth glide has no effect.
• Can a creature use the ability earth glide to avoid being pushed into a wall? Only if the creature can itself move some distance via its burrowing speed into the wall. As a reaction to being pushed? No.

Note that the rules for extraordinary ability burrow were omitted from the Pathfinder Core Rulebook.