You cannot activate magic items with Fast Hands
The section on activating magic items specifically calls out this case:
If an item requires an action to activate, that action isn't a
function of the Use an Item action, so a feature such as the rogue's
Fast Hands can't be used to activate the item. (DMG 141)
The following items from the DMG are included and useful:
Instruments of the Bards
Moonblades, but only if you are neutral good
Robe of the Archmagi (but only if its alignment matches) (15+Dex AC and bonuses against spells)
Rod of Resurrection
11 different kinds of staves
Tome of the Stilled Tongue (bonus action ...
As mentioned by Krzysztof Skibiński, a spell book is not a magic item. The Thief Rogue's sub-class ability Use Magic Device allows your rogue to use a magic item that they normally would not be allowed to use.
For instance, a Rod of Resurrection (DMG, p. 197) normally only requires attunement by a Cleric, Druid, or Paladin to be used. This ability ...
Wizard's Spellbook is not a magic item. It's their Spellcasting class feature that allows them to prepare spells from their (and only their) book, which they can later cast.
As a student of arcane magic, you have a spellbook containing spells that show the first glimmerings of your true power. (...)
Preparing and Casting Spells
You can use Fast Hands to equip a shield.
In the Player's Handbook, on page 193, the Use an Object action says:
When an object requires your action for its use, you take the Use an Object action.
A shield is an object, and donning or doffing a shield requires an action, so it seems to fall under Use an Object, just like any other object use that ...
The spice pouch requires an action, so it doesn't work with Fast Hands
The description of Heward's handy spice pouch says:
While holding the pouch, you can use an action to expend 1 of its charges, speak the name of any nonmagical food seasoning [...]
— Xanathar's Guide to Everything, p. 137
That action is a special action option given by the ...
Thief Rogues do get a Dexterity Ability Boost
All classes, regardless of any other choice they make, get an Ability Boost in their Class (or Spell) DC Ability. The Thief gives up the option to choose Strength or Charisma (granted by the Ruffian and Scoundrel rackets respectively), and must take Dexterity for this choice.
There is no interaction - you aren't using it, you are donning it.
Using an object covers:
You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. When an object requires your action for its use, you take the Use an Object action. This action is also useful when you want to interact with more ...
Donning or Doffing a shield requires an action
Donning or doffing armor is separate from the "Use an Object" action. Notably, a shield is the only kind of "armor" that takes 1 action to don or doff. The rules for donning and doffing are pretty clear:
Don. This is the time it takes to put on armor. You benefit from the armor's AC only if you take the full ...
The key ability for rogues says "Dexterity or other". As you noted, the "other" options come from your racket. Therefore, no matter which racket you pick you may still choose to have dexterity be your key ability and get a boost to it. The specifics of the thief racket don't change this.
However, to answer your question more directly, the thief racket ...