1. Analyze the stats of the card (HP, Weakness, Resistance, Retreat cost).
90 Hp on a fully evolved pokemon is ok and it's retreat cost isn't terrible if you're just planning on keeping it active, but might be costly in an emergency. Weakness to Psychic isn't bad since most psychic pokemon have weak attacks.
2. Analyze the attacks (and/or Poke-Powers, Poke-Bodies, Abilities) of the card.
Dream eater does 90 for 2 energy.....AWESOME. The only downside is that the defending pokemon needs to be asleep in order for it to work. To help it, Hypnotic Ray is a 1 energy attack that does 20 damage and causes sleep. However, the fact that, even if you don't take into account switch, super scoop up or anything similar, the defending pokemon will only be asleep on your turn once every 4 turns when you use Hypnotic Ray, meaning you're doing on average less then 40 damage per turn (by comparison, Sawk from the same set is a basic which can do 40 damage each turn for 2 energy).
3. What combos can you use it with? How so?
To get this card to work, you need to have it asleep on your turn. The only card I can think of in HGSS that does that is Hypno, whose power can make the defending pokemon asleep on a coin flip. If you get out two (or even three) of them, then it's very likely that you can use Dream Eater on your turn. The downside is that it uses up bench space, and creates a very desirable target for your opponent to either snipe or drag into the active (Hypno also has a retreat of 2), and if one goes, your chances of using Dream Eater are lowered. Since you're doing 90 damage as well (enough to ko most basics and techs but not the biggest attackers), cards such as Pokemon Reversal, Pokemon Circulator and Pokemon Catcher (if it's released) can let you take easy prizes.
4. What techs can you use to combat the weak points?
Switch is a must in case Drowzee or Hypno ever make it in the active spot. Recovery cards might also be needed to get Hypno's out of the discard pile back on the field (otherwise the deck will begin to suffer). Also, A fire type pokemon such as Darmanitan is needed in the event that you come across a Steelix Prime which destroys your main strategy (It's body and resistance pretty much makes it Immune to Musharna).
5. How's the artwork?
Meh...
6. Give it a rating, and explain why you have given it that rating. You can also rate the card by rating the thread itself (out of 5 stars).
3/5. In MD-BW it can potentially be a competative deck since there's a lot more support for sleep (Darkrai and Darkrai G) as well as other techs and cards which can be added to get around weaknesses. In HGSS-BW it's still one of the best attackers with the right support, but since it requires a bit of set up, as well as some luck, I don't see it making it's way into one of the top decks next year unless a more reliable way to cause sleep comes up.