I don't understand why "första" is plural in this sentence.
You also add an -a to make an adjective definite, and you use the definite form after a possessive adjective like min or din. Första is also how you say "first" as an ordinal number.
Does det finns work here?
No, that would be like there is my first week here in English.
It will be in April!
Could this be translated as "This is my first week here"? Or is there a different way to convey that?
'This' is det här or detta.