Is it okay if I don't finish a sentence?
Is the sentence you aren't going to finish long?
No, I like to end my sentences with an ellipsis (...)
While you can use ellipses when communicating with friends, it isn't appropriate to do so when you are interacting with others professionally. You should try to use proper grammar and finish your sentences as it shows that you are a careful and thoughtful writer.
I feel too lazy and don't care.
Using poor grammar can be considered rude since it makes the recipient work harder at understanding your thoughts. You'll be required to use proper punctuation when typing in a professional manner, so you might as well get used to it now.