You have to become a member of the mages guild. For you to do that You MUST do a series of misions.
longsword, nowhere, but most mages guild halls have one in the open somewhere
many traders will sell some lesser effect scrolls, the mages guild is free to join and will provide you with many spells and scrolls and when you enter an oblivion gate many deadra will drop useful scrolls
The mages guild in skingrad
the mages guild halls usually have someone who can recharge your weapons. but it can be expensive. you can also find varla stones in Ayleid ruins that will recharge all the enchanted weapons in your inventory.
Yes Such as, The Mages Guild The Fighters Guild And several other things such as the Imperial Legion or Imperial Cult and many more.
To access the big room in the Arch Mage's Tower in "The Elder Scrolls IV: Oblivion," you need to complete the "Recommendation" quests for all the Mages Guild recommendation. After earning the title of Arch Mage, you'll receive the key to the tower, which allows you to enter the big room where various magical resources and items are located. Additionally, the room is accessible once you have completed the main Mages Guild questline.
If you've been kicked out once before, and re-accepted, there is no way back in if you got kicked out a second time.
Assuming you mean spell scrolls, both merchants at the Mystic Emporium in the Imperial City Market District sell some. Check the Mages Guild branches in each city, they have scroll selling merchants too.
every city but kvatch and the imperial city in the imperial city is the univirsity
They are in all of the cities mages guild mostly or in the ARCANE UNIVERSITY.
Go to the main mages guild in the imperial city, and look for the head guy. He will give you a quest saying you need to get 20 Dragon's Tongue and 20 Redflower.
you'll find it in the mages guild quests anyway, but it's NNE from cheydinhal, i think.