The champs are not labeled as damage dealer, debuffer or healer in the game. But a lot of categories are still quite obvious. 

A healer is a champ that can heal your teammembers. Read the skill description to get to know. For example High Elves epic Thenasil, his A2 skill: Places a 60% [Increase DEF] buff on all allies for 2 turns. Heals all allies by 25% of this Champion’s MAX HP. His job is to heal your teammembers. Crit rate and crit damage don't help to do so. The heal is based on his max hp, 25% of his hp is the ammount of healing, as you can read in the skill description. Thenasil with 10k hp heals for 2.5k hp, Thenasil with 60k hp heals for 15k hp. This champ gets better, the higher his own hp is. You want a lot of speed on Thenasil as well, so he can use his healing ability more often during the fight.

A debuffer is a champ who can put debuffs on your enemies. Warmaiden can put decrease def on all enemies, she is the best example for a debuffer. She needs enough accuracy to land her debuffs. You can increase her damage in addition to that, but that's secondary. If she doesn't land her debuffs, she is useless.

A damage dealer is a champ with high base stat of his damage increasing stat (for most champs attack) and high damage multipliers. Like kramaswamy allready said, you can find the damage multipliers on sites about the game like Ayumi. There you can see that Warmaiden has a damage multiplier of 4 on her A3 skill, her base attack is 1321. That results in a base damage of 1321 x 4 = 5284. That's ok, but not overwhelming. I would not consider her as a damage dealer. 

Compare to, for example, Trunda, the best damage dealer in the game. Trunda has a base attack of 1608, her A3 has a damage multiplier of 3 and can hit twice. Base damage of that skill is 1608 x 3 x 2 = 9648.

Calculating the base damage of a skill is a good first step to see if your champ can work as damage dealer. There are other factors as well, special abilities of a skill like ignoring defense (Royal Huntsman), allways critical (Ithos) or stuff like that.

Let's go back to Thenasil, is he a damage dealer? His A3 can attack all enemies, and it has a quite high damage multiplier of 4. But his base attack is so low, only 991. So the base damage of his A3 is only 991 x 4 = 3964. Compare that to Trunda's 9648. Obviously Thenasil is not a damage dealer. And he doesn't have to be a damage dealer, he is a healer.

Practically speaking, you can use the in-game designation of "support" to filter pretty effectively. Most support champs are either healers and buffers, or debuffers.

But more generally speaking, it's usually not worth putting champs into tight buckets like that. Some are obvious - Big'Un is clearly a damage dealer, Arbiter is clearly a support healer/buffer, Serris is clearly a debuffer. Others are less so. Sinesha is arguably a healer, but she also has a very strong attack, and as a debuffer has the rather unique ability to put skills on cooldown. Ninja is arguably a damage dealer, but many build him for his AOE freeze as a debuffer instead.

As for your second question - Warmaiden is typically used as a debuffer, so you would generally call her support. Her main use is her AOE DEF down debuff. The stat line seems fine, but most people build her to use for arena, and if that's your goal, you also need to make sure she's fast enough to go immediately after your primary speed booster(s).

(Edit: Didnt see two had already answered)

Raid stamps the champions like: Attack, Defense, Support. But it is just a guideline. This game is complex but what role you champion is very much depends on where you use her and with whom. So the short answer those categories are not important.

And the long answer:

My suggestion is to look at the champions skills at first and use your own judgement or maybe some videos on youtube to decide which role you champion can play.

Based on your question im guessing you are relatively new to the game. So the most important areas are probaly, campaign, Dragon dungeon, clan boss, Classic arena.

Campaing: your goal is to be able to beat stage 12.3 on brutal with 100% winrate preferable decently fast. For that you need a champion that regularly "attack all enemies" Your starting champion will be fine. You need high damage and good speed. Everything else is not important unless you use the champion in other areas.

Dragon dungeon: Here you need more roles. The harder the dungeon is for you the more you need a diverse set of roles.

Healer: A champion that can heal in some way. since a revive always bring champions back with health they can be put in this category.

Common examples: Scyl, Broadmaw, Reliquerary tender

Debuffer : A champion that land negative effects (debuffs) on the enemy.

You can in generel divide them into two categories - offensive and defensive debuffers.

Common for both is that Accuracy is important. just like crit rate you need enough accuracy and too much does not help you in anyway. Rule of thumb has been suggested to be 10* times the level of the dragon dungeon. If you see "resisted" often on the enemy you probaly need more accuracy. Note that there is always a minimum of 3% chance of resisting. Also note that weak hits can not land debuffs so affinity can play an important role for debuffers.

Offensive debuffs:

Decrease defense, poison, hp burn, weaken

Most commonly you want decrease defense. But poison is really good on dragon and clan boss aswell.

Common examples: War maiden, Kael, Athel

Defensive debuffs:

Stun, fear, freeze, provoke, decrease attack

Common examples: Gnarlhorn (he is really good), Stag Knigth, Scyl, Miscreated monster

Damage dealers:

A champion that hits hard. Often someone that does "attack all enemies" often in his skills. In some content champions with hp burn or poison works well as damage dealers aswell.

A note on damage dealers is in the early stage attack based damage dealers can be really hard to keep alive without good support. So if you can finde good defense based damage dealers that might be useful early on.

Common examples: Your start champ, Ninja, Armiger, shield guard

These are very good writeups and worthy of some study.

My disappointment has to do with the tricks that have come into the game that make all the analyis less important, Namely, things like unkillable buff, and revival of dead champs, make the whole thing very artificial. Just other things in this game you have to be lucky enough to have. Pretty annoying to go into arena, doom tower, factions and have all your opponents popping back up over and over.

So you might say all you need is a block revive champ, unfortunately that is another topic of luck cuz you just cannot buy one off the shelf.