"Enter the first door!"
Translation:Kaingie mlango wa kwanza!
They are two different uses of the same -ka- morpheme, with different meanings and different constructions.
Nilifika na nikaingi
a mlango wa kwanza: I arrived and (then) entered the first door.
e mlango wa kwanza!: Enter the first door!
In the first sentence it is the so-called narrative tense: I did 'this' and then I did 'this' and then... In the second sentence it is used as an imperative tense (using the subjective): this is stronger (and less polite) than just saying Ingia mlango wa kwanza.
The ordinal numbers, when referring to something, always start with -a (wa, ya, la, cha, vya, za etc.). Moja "one" and mbili "two" have the unique forms -a kwanza "first" and -a pili "second", but all the others are shown only by adding the -a before the normal number.