Is there a difference between "multumita" and "gratie"?
Not really. "datorită" can also be used here.
Out of this context, you should keep in mind homonyms: "mulțumită" is also the feminine form of "pleased", while "grație" can also mean "grace".
Why not "... o muncă" instead of "o slujbă"?
"o muncă" indicates "an activity" and not a job. This meaning is taken by "muncă" only in combination with "la": "la muncă" when the sense is "to the job".
What about "un loc de muncă"?
This is a good option. When a correct answer is not accepted you can report it using the flag. All the corrections are made based on user reports.
I wrote datorită and was not accepted. I reported it.
Super! Thank you!
Why not "o treabă"
"Grație (Datorită) ție eu am o treabă." is a correct sentence but has a different meaning: "Thanks to you, I have something to do."