Swahili speakers often leave off "ni" when the meaning is clear. I believe this is only for first person
Yes, this is for first person singular only in present tence. There is however a gnomic tense with the same first person singular form as the shortened present tence.
What is a gnomic tense?
It's a verb form that's used for "timeless" or "tenseless" situations, such as things that are always true or eternal.
Why also naanza? you cant know the person right?
It's just a shortened form of ninaanza. Still 1st person singular present tense.