Two Problems

Hello. I'm rather new to the game (only played for a few months, around 9 days total playing time on my character) and I believe I've got a relatively decent grasp on the game. My main profession is an Elementalist.

I've beaten Prophecies and recently beaten Nightfall (I skipped Factions because of all the negative comments I've heard about it) and there are a couple areas I am struggling hardcore on.
The first is the mission "The Last Day Dawns". So far I've only gotten up to the third group before wiping. I can never keep the NPCs alive and when the NPC priest dies its usually game over. Its incredibly frustrating because I've tried a diverse number of builds from water elementalist to air, to using fire with Winter and changing hero builds (as well as switching heroes around.)
I've done this mission so many times I can barely keep count...think its 25 times but I can't be sure...

Sometimes I often regret rolling an elementalist because I usually feel underpowered. I either feel overpowered at times, or simply very gimped. I wish I felt my class was in the middle at all times.

The second problem I have is the Domain of Anguish. I noticed they were elite missions, but I decided to try it anyway. Whenever I pull a group in the city however, I literally get torn apart unless I get lucky and down a mob or two. The farthest I've gotten here was four groups in.

I know I run with heroes and that can be a disadvantage given the brainless stupidity some of them exhibit (trust me, I've often felt like strangling them because of behaviors like deciding to run into an enemy pack to resurrect someone when I've retreated) however I don't like to run with players given people try to wrangle power of the group; not to mention the elitist attitudes of some players. I prefer to control how my group runs.

Any tips would be greatly appreciated.

Edit - I'd like to add that I also (mistakenly) ran from Yak's; not only was it a long run going the long way, but after I went up the back entrance and destroyed two groups, the last two groups bunched together and I had to give up after multiple wipes.
I won't even try the run from Kryta...

For HM area's, try the ER Infuse. Link.

Elementalists tend to shine as healers in HM, drastically reducing damage dealt to allies while spamming insane heals and buffs.

Other than that, Mesmers and Necros does much more damage with spells. Why? Because Hexes ignore armor, can be AoE, AI does not react and can be triggered multiple times in less than a second.

Your out of luck when it comes to damage, but you have the best healing profession in all of Guild Wars.

^That's pretty much the answer.
When you pick up the prof labeled as "THE caster damage" you can't know that you'll find yourself with the worst one in high end pve, and instead have the best prot/healer.

If you prefer you can try carry utility, but others can do it way better(eg:shell shock vs. weaken armor).

For dmg you can try exploiting pve skills (EVAS, FH, YMLAD) with AP, plus a bit of air spells, but is still sad have to rely on that.

P.S: before try those hard/end stuff, i'd finish faction too. Might not be te best campaing, but have anyway his bunch of really useful skills (included pve ones) and is still unexplored content for you.

my only question is why play an mmo if you dont want to play with other players? doesnt that defeat the whole point?

If you find an area or level where Ele isn't working for you don't think of yourself as just an ele you also have a secondary class that you can change at will.
You are a spellcaster with a huge energy pool.
Mesmer or Ritualist work for me though even in hard mode I concentrate on a fairly standard Earth build and see myself as the party defender.

I choose where we fight and use wards to alter the ground to benefit us Ward against melee ward against foes churning earth etc.
For overkill you or a hero can throw in necro circles and the enemies are all being degened as well and the party are gaining health energy or both.

And I wouldn't miss out on Factions not only is it pretty enjoyable to play but the assassin, ritualist and their skills are great.
I tend to play a defensive war in pve so its plenty of necro minions and ritualist spirits to do the hard work.

Domain of anguish is indeed an elite area and even in normal mode, it's a lot harder then many area's/mission in hard mode.

My main character is an ele, and both as healer, but also as heavy damage caster I can do a lot.

I think the answer to you problems are in the details. Both things you've mentioned are hard. So look at your own build, but also to that of your hero's. look at your weapons and your hero's weapons, and don't forget the runes and insignia's.

Factions isnt really that bad - i used to hate it like mad and stayed off doing it for 2 years but once i got used to kaineng zones and got into lux/kurz areas factions really opened up and i still go thru it now.
Kaineng area is the most confusing - prophs and nightfall are easy to navigate and is what id call single level but kaineng area is multi level where you would go up or down a ramp .Its this which gets ppl as some zones the exit seems near but you have to travel up and down etc for say 15 mins.
Hero wise - its usefull with any hero builds to know what to set them on - attack/guard/avoid and it sounds like yours are set on attack which means they attack anything in range and will follow/run to foes to kill them.
Remedy would be - check guru`s hero section and check gwpvx.com for their hero builds and you can see examples of team/hero builds that work.
Remember a chain is only as strong as your weakest link - so ensure all heros are runed correct for their build and have correct weapons and settings.
Also be aware that some builds for teams are done for specific professions - meaning that there are team builds for all caster teams , ones for teams with say 3 melee and rest casters but a team set for melee wont always work on a caster only team as some skills may be there to boost the melee and is wasted on a caster.

Halfies - some ppl who are new to gw may not want the hassle of finding pug teams or being told they suck because of lack of skills.Heros do give a new player time to adjust to gw at their own pace rather than being kicked from a team due to skills.Not everyone will help or want a newbie in team ( when you have new players who wont listen or do what told you can understand why ).

You know, it really annoys me whenever people come here for advice on eles all they are told is 'damage is crap, run E/Mo' instead of trying to help the person. If you want a brainless bar then the E/Mo bar is perfect but, to me, a game is meant to be fun and facerolling isn't my idea of fun.

I have done everything NM and HM on my ele and have never faced anything that I couldn't do AND I used ele skills. There isn't a build that's perfect for all areas, you need to look at what you're facing and adjust yours and your heroes build to suit.

The 2 things you mention, the quest 'The last day dawns' and DoA, are both quite tough but for DoA you will you probably have to change your hero set up so that you have plenty of heals as well as damage.

http://www.guildwarsguru.com/forum/campfire-f17.html If you have time to look through the PvE section on this forum, I seem to remember there being a discussion on heroes used for DoA NM.

http://www.gwpvx.com/PvX_wiki This site has lots of builds for yourself and your heroes.

And like Spritz said, Factions really isn't so bad. The city is a bit of a maze but once you get out of there it's much different.