This is mostly targeted at 4 person dungeons - but after being in a few where "newbies" have and haven't learnt things, this is my take away...

I think you are trying to be polite and concise in how you are phrasing things, but I don't think you are being polite for the recipient.
I also think 'vets' as you call them need to remember that for some people this is a casual game where they may only play a couple of times a week and be newer to MMOs.

Advice

If speaking with somebody that's the same language I often start off by saying something like

"<name>, <class> is one of my favourites! May I offer some advice that I found extremely helpful and bumped up my <dps|healing>"
Occasionally followed by
"If you're unable to type, please jump once for yes, twice for no!"

By putting it in their hands to say "Yes" I find people more accepting of advice. Especially if you can relate that you too were in their place once.

Also - it's a game. Being told what to do or how to play your class is not fun for the receiver and I don't find it polite when I read it. If they say "No", they likely weren't going to listen to your advice (you may be lucky and they would have looked into it afterwards).

Controller/console players
Whilst on PC you may have all your spells/skills visible (and clickable) at a moments notice some console/controller players will have what they consider their main skills on the minimum amount of cross hotbars.
I'm not offering a solution to this, I'm just saying this can be a reason things like Sects may not be noticed.

Boss Mechanics
Regarding mechanics, not everybody is going to go and watch a trial/dungeon guide. They want to experience it first hand, see if they can figure it out themselves.

I find if you have a new player bonus you can offer "Would you like me to explain the mechanics, or would you like to try it first?"
You may be fine, get through it and they would've worked out most of it by themselves. They might get stuck and say "What went wrong?".

Alliance raids - Inform your party of mechanics. "A - adds, B - belly, C - chains" means nothing if it's your first time. If it's not your first time, you probably already know the ABC.
i.e. Scyrus tower: "Reminder: If you get purple tether, please run to X, if you get fireball, bring it to frozen player if possible! :) ", "BTW When he casts Curtain Call, get behind some ice!"

COMMUNICATION
If possible, communicate. Not everybody has keyboards, but you can work it out. If you're tank and unsure of healers abilities, ask "Med/Big pull?", if no response, try medium pulls and get bigger.

You can make or break peoples experience in this game with how you communicate.