In Mage: The Ascension, if I create a wonder or complete a task for someone who will pay me fifty thousand dollars while I have zero dots in resources, do I need to spend experience in order to actually make that part of my character? Or do I gain it without spending experience through my effort as a player?
That's going to vary from game to game. Different STs run it in different ways.
The "middle-of-the-road" version that I've heard is that paying exp means that the background/merit is protected to a degree, while if you don't pay exp it can be taken away by the whim of the plot, but it varies. Talk with your storyteller.
As Ben Barden said, this varies by storyteller. The Chronicles of Darkness: Mage: The Awakening includes a "sanctity of merits" rule which essentially says that if a player pays starting-dots or experience for a merit and the story removes the merit, then the experience or dots are refunded and may be spent again.
But if that was ever formalized in the original World of Darkness or Mage the Ascension I am unaware of it.
My approach varies slightly from Ben's when I am the storyteller. A player may spend experience during downtime to acquire any merit they want and create any, or even no, background for how they got the merit. If the story then removes that merit at a later time, the experience is refunded.
Merits that are acquired during play are valid without spending experience and may be freely used. However, the player normally must overcome some challenge to get that merit and it may come with consequences. The merit dots also will not be refunded if it is later lost.
On page 336 of M20, Resources is described as "financial credit, cash flow, and property." In the same book, on page 322, the various levels of Resources are defined using levels that indicate the degree of financial stability you have—the lowest of which is "a middle class income."
"Fifty thousand dollars in a lump sum" isn't the same thing as a regular salary. You can just have a briefcase of money — it doesn't necessarily amount to a background's worth. If you manage to turn it into a steady gig, then spend the XP — or ask your ST — to acquire the Resources background.