Devotion is defined in the comprehensive rules as:
700.5.: A player’s devotion to [color] is equal to the number of mana symbols of that color among the mana costs of permanents that player controls. A player’s devotion to [color 1] and [color 2] is equal to the number of mana symbols among the mana costs of permanents that player controls that are [color 1], [color 2], or both colors.
So to address each of your questions separately:
1. What is the devotion to blue from a Awonken Horror?
Awoken Horror provides no Devotion. Double faced cards have the converted mana costs of their front face, but do not have a mana cost(emphasis mine).
711.4b: While a double-faced permanent’s back face is up, it has only the characteristics of its back face. However, its converted mana cost is calculated using the mana cost of its front face. If a permanent is copying the back face of a double-faced card (even if the card representing that copy is itself a double-faced card), the converted mana cost of that permanent is 0.
202.1.: A card’s mana cost is indicated by mana symbols near the top of the card. (See rule 107.4.) On most cards, these symbols are printed in the upper right corner. Some cards from the Future Sight set have alternate frames in which the mana symbols appear to the left of the illustration.
This means that even though your opponent can target it with cards like a non revolted Fatal Push, there are no mana symbols to count to determine devotion.
2. Does a suspended Deep-Sea Kraken give devotion?
No. Devotion only comes from permanents you control. While exiled Deep-Sea Kraken is not a permanent (emphasis mine).
110.1.: A permanent is a card or token on the battlefield. A permanent remains on the battlefield indefinitely. A card or token becomes a permanent as it enters the battlefield and it stops being a permanent as it’s moved to another zone by an effect or rule.
3. Does a token copy of target creature given the same devotion/(have the same mana cost) of the original?
Yes. Token copies inherit all characteristics of the card they are copying, including mana cost (emphasis mine).
706.2: When copying an object, the copy acquires the copiable values of the original object’s characteristics and, for an object on the stack, choices made when casting or activating it (mode, targets, the value of X, whether it was kicked, how it will affect multiple targets, and so on). The “copiable values” are the values derived from the text printed on the object (that text being name, mana cost, color indicator, card type, subtype, supertype, rules text, power, toughness, and/or loyalty), as modified by other copy effects, by its face-down status, and by “as . . . enters the battlefield” and “as . . . is turned face up” abilities that set power and toughness (and may also set additional characteristics). Other effects (including type-changing and text-changing effects), status, and counters are not copied.
4. Does a naked Phyrexian Metamorph give 1 devotion?
Yes. Phyrexian mana counts towards devotion.