Why is "a service" "en service" but "the service" is "servicet". Should this be "one service"?
I don't know where you get the servicet from; the definite form of service is servicen so its gender remains intact.
a service = en service
one service = én service or een service
There are two distinct nouns called 'service'
One is common gender (the labour/action you perform for another person)
The other is neuter gender and is a common word you can use for cutlery, plates etc.