2 part question
I was appointed Thrane ( thane?) by the Jarl, and I assumed it would come with a room or house? I have been up and down all the streets and houses and can not even find one for sale ( even checked the minimap)

With this appointment I received Lydia the housecarl ( I have been calling her hot carl) as a companion/follower....we climbed the mountain to see the grey beards, I ran from the Troll like a little girl, and she eventually followed soon after...mission complete, saved, looked for her in every place...she is gone. OBVIOUSLY I can not enlist any other person til she is accounted for and if she was dead it would be easy...shouldn't she have a beacon on the map?

PS yes I have looked at the other threads, but no one is answering them either so I just hope someone knows, or Bethesda makes a patch soon

Try entering a dungeon. Followers usually spawn right behind you when doing so, unless she's dead of course.

( part one )The house is called the Breeze house ( 20 ft or so by the main entrance to whiterun ) and when bought lydia will be there..

( Part two ) If you have the breeze house.. she might be there or she's caught on something on a mountain or where ever you left and need to find her.. I had the same problem in Oblivion..

that's why I haven't bought her along because I don't want her getting stuck on anything like a twig or a sm rock..

before you have a residence, she lives in the castle. Try checking to see if the game got confused and sent her home? She'll be hanging out near the entrance or sitting at the table.

Once you buy a home she'll sit there patiently and wait for you. Oddly enough, in your bedroom

If you fast travel anywhere, your current companion will spawn next to you. If it doesn't happen, she's dead or on stay somewhere. Or at home.

The guide says "any lethal blow inflicted on a kneeling companion will kill them ie forever" but these guides tend to be wrong after the 1st patch...

I've also found that if you sleep in a bed she is usually right there when you wake up

To buy a house go speak to Jarls dude at Dragonreach that works for him with the balding head, he stood to the left advising Jarl when you spoke to him.
You need $5000 to buy the house. As others have said, its Breezehouse and the second on the right when you enter town.
Lydia may be there, but more likely she may be back with Jarl at Dragonreach.

Great, thank you to all...I will go try a few right now. Dungeons, sleep etc

Missing Lydia reminds me of my missing horse.
I slew a dragon with my Ancient Nordic Greatsword and the scaly beast landed on my trusty steed, causing her to evaporate.
Obviously just fast traveling makes it re-apear at the stable, but made me lol none the less.

AFIK, Lydia can't die on standard difficulty. I've watched her go toe to toe with Dragons and Giants, go down (i.e. kneeling position) get finished off, then get right back up. When Lydia is finished off, it takes about a min for her to get back up sometimes, about 10 sec for her to return from Kneeling.

I'll sometimes jump on a horse and go for a ride with her in tow. She follows by foot at max NPC speed, so it can take some time for her to catch up (I road straight to Solitude from dragon reach by horse back, she showed up 10 to 20 mins after I got there). She should fast travel and join you after zoning always automatically if she's still following you. If not, she'll go back to your home, or sit Dragonreach if you don't own the Breeze Home untill you come back for her (Check the Jarl's side or balcony of Dragon Reach if you can't find her there).

lydia can die. I know because i moved her lootable corpse to a spot towards the top of high hrothgar and placed her shield and sword on her burial style. Frost Troll took her life.

I did that too (kinda burial style) the first time a giant killed her, cept I took back her magic sword and used a basic Nord sword. Then she reappeared back at DragonReach without weapons. Is there an ingame option that can be changed to allow them to die?

Yeah, mine is dead. poor thing xD

Check Dragonsreach. Lydia appeared there after I lost her.

Dungeon- No workey
Sleep/rest- no workey...either in an Inn, or or waiting in random area

still not enough chedda for breezehouse

If she was dead, I would be able to recruit someone right?

she is not at dragonsreach, or whiterun...

(does anyone know where her quarters are in dragonsreach?)

For any on PC...

open the console
prid 000A2C94
resurrect <------ if you think dead
disable
enable
moveto player

I had to use this because for some odd reason her death prevented my character from getting married to anyone.

She can die if you keep letting her get hit after she drops to one knee, she will stop and htey will stop focusing her but she can indeed die.

According to the strat guide, it says if "You [the PC] Inflict fatal damage" then the follower will die. Maybe only the player can trully kill a follower?

Dunno, but I haven't seen a NPC that can kill Lydia yet (And I've puter her up agenst some real monsters).

i have a dog companion and i keep losing him, then i have to load a old save. its a pain i hope they fix this, i also left him in riverwood and did a quest,when i came back he was gone? poor doggy maybe a dragon ate him

I just went back to the places I had been and found her where I told her to wait.

You either told her to wait somewhere and forgot. She died. Or she's in Dragonreach's main hall. That's where she goes if you get seperated.

Think yourself lucky, my Housecarl starting attacking Vilkas/Skjor when they were testing how strong I was, [censored] just didn't stop followed him all around the Companions House and smacking his ass, I feared it could get me in trouble so I was forced to execute her.

Luckily en route to High Hrothgar I found a young gent called Golldir, he seems pretty solid, but I sent him away after he 'accidentally' pushed me off a tower and into a group of Bandits I was sniping - tit.

my poor lydia died fighting a dragon priest. the service for her was short but very touching. she was well liked.