Yes, Jordis is in Solitude. She is only available once you become thane. Yes, The Proudspire Manor is a purchasable house for $25,000 Septims.
Here is a guide to becoming thane of Solitude.
"Talk to Falk Firebeard in the Blue Palace, and he will give you the quest The Man Who Cried Wolf, summoning you to investigate lights and sounds coming out of Wolf Skull Cave which is located in the mountains west of Solitude. After completing the quest, talk to Falk again and he will reward you. You may then speak directly to the Jarl herself, and she will thank you and give you one more task.
She will ask you to place Torygg’s War Horn on the Shrine of Talos as a tribute to her late husband. Take the War Horn to the specifed Shrine and place it at the foot of the statue of Talos, then return to Elisif for your reward.
After you have completed this task go back and talk to the Jarl. She will invite you to be a thane of hers but in order to be a Thane, you must first own property in Solitude and be known throughout the hold. This property can be purchased from Falk for 25000 gold pieces. Being known throughout the hold is done by helping out 5 of the citizens with their miscellaneous quests. Once you buy the property and help the citizens, go and talk to her, and she will appoint you to be a Thane of Solitude.
You will also be given the Blade of Haafingar.
Note: Some time after you clear out Wolf Skull Cave, you will receive a letter from a courier asking you to speak to Falk once more. This is a quest to hunt down Potema's spirit, The Wolf Queen Awakened, but is not required to become Thane."
There is a bug that can occur. Make sure you go through Quest line to become Thane and purchase the house. After I purchased the House I believe I talked to Elsif the Fair afterwards she told me to become well known before I can be appointed Thane. This is where the misc quest "Assist the people of the hold" comes up. You can do a view misc before speaking to her after purchasing the house. But I recommend to speak to her immediately for the quest to appear, once you have done all 5 misc quests. Then you can talk to her to become thane.
The Bug that can occur, happens when a person does the 5 misc quests ahead of time. Thus glitches the quest from completing.
Also, after purchasing the house. If the Jarl Elsif the Fair doesn't say anything just in case that happens. Just wait two days or so. It hasn't happened to me nor have I heard of it. But just in-case something does occur.
Hope that helps and let me know if you're were successful with becoming Thane of Solitude.