You wanted constructive critism so I'm just going to go ahead with grammatical "constructive critism", xD...
So, I'll post in red places that are wrong, and maybe tell you the reason and why it is wrong (please don't be offended!):
Rune's internal clock told her it was about two hours after she had woken up that everyone else was awake.
The first person to wake up after Rune had jet-black hair, only a bit shorter then Jokester's. She introduced herself as Emily or Em.
About thirty minutes after Emily woke up, a girl with black hair and green eyes woke up. She and Emily resembled each other so much that (could be mistaken meaning, since it's a run-on) Rune knew she was bound to mix them up if she didn't remember that Livvy was the one with a few gray steaks through her hair.
The last to wake up was a boy with the name of Cain. He had wavy blond hair that he kept running his hand through. He had a single star tattoo on the nape of his neck. Just after Cain had finished introducing himself, a hidden speaker crackled to life.
"Glad to see you're all awake," a deep female voice declared.
"Woah, she can see us?" Terrance muttered, taking a minute to look around the room.
The voice continued, ignoring what Terrance had said. "I am the Riddle Master; your guide, your savior and possibly your demise. There is no point in an escape plan seeing as you will eventually be set free, though from life or this room I cannot tell."
Emily shuttered (shuddered, spelling mistake), but Kiero was soon at her side in hopes to comfort her. Jokester's eyes lit up when she saw the two and nearly squealed for joy.
Ridge turned to look at everyone with a thoughtful gaze, trying to find out who would be the most useful to him. A small smile appeared on his face when his eyes landed on Rune, who shifted uncomfortably with the Riddle Master's words.
"Your only hope of surviving," the Riddle Master continued. "Is (1) to answer a series of questions correctly. Answer a riddle correctly and you will be rewarded. Answer incorrectly, and well, there's a slight chance of death. If at any point you desire for a riddle, simply say, 'The Riddle Room needs a riddle.', and I will give you one. Would you like your first one now?"
(1: This is a quotational error: After "continued" is a comma because the entire sentence is "Your only hope of surviving is to answer a series of questions correctly", not "Your only hope of surviving. Is to...". Because the sentence is cut off in the middle, it is a comma.
"Yes!" Cain blurted without thinking. Livvy and Jokester gave him a glare.
The Riddle Master Chuckled. "Such enthusiasm! Alright, I'll start easy, but only Cain can answer it. No help. What gets wetter the more it dries?" Rhythmic elevator music replaced the Riddle Master's voice.
Rune looked down. She could only wait and hope that Cain got the right answer. If he didn't answer right, she was going to kill him. That is, assuming he is (2) still alive afterwards. After all, the riddle was incredibly easy.
(2. Present tense error; since you are using past tense be careful of these places.)
Suddenly, a soft trickling noise filled her ears. Rune's eyes shot up and she noticed tiny holes in the walls that were quickly filling the room with water. She gasped and decided to raise the alarm.
"Uh, hey guys, the room is filling up with water," Rune declared as the water reached ankle hight. "And fast."
Cain panicked when he peered down at the water, suddenly forgetting the riddle. "Wait, what?"
Emily screamed, "We're all gonna die!" Her face went pale as the water reached her knees.
"Cain, can you please just answer the riddle already," said and (an) annoyed Ridge. He held his hands just above the surface of the water, which by now was waist-high.
"Oh, uh, right," Cain cleared his throat and answered, "Wait, what was the riddle again?"
Rune sighed and facepalmed. By now, the water was up to her armpits. "What gets wetter the more it dries?"
"Oh, you mean a towel? I know, I need one too," Cain responded.
A chime sounded from the speaker and the music stopped. "Correct," the Riddle Master announced. "You have just won eight towels and eight meals, dessert not included."
Rune could hear Terrance mumble a complaint and couldn't help but smile. It helped that the water was now draining through tiny holes in the floor.
About five minutes later, there was not a single drop of water in sight, only orange juice.
Everyone had received a meal consisting of pancakes, bacon and orange juice, along with towels that came from seemingly no where. Rune had just turned around to find eight neatly folded towels. She didn't know where they came from, but hey, she wasn't complaining.
Most people were having a joyful conversation that were mostly lead by Livvy, while a few, including Rune, decided to focus on the meal. But that wasn't the only thing Rune was focusing on.
She was halfway through her meal when she was plagued by one thought.
Was she going to die here?
Sorry, this is probably highly unhelpful. I like how you put vivid description and very nice character thought process in it. Keep up the good work! I'm really looking forward to the next chapter. :D
By the way, I'm only so good at proofreading. :P