Translation:I am inviting many friends to my party.
Yes. It is the personal "a" that is used when the direct object is a person or pet. https://www.thoughtco.com/the-personal-a-preposition-3078139
Yes, I know what you mean. I learn like that also. Repeat, repeat, repeat and soon I just know what sounds right, even though I may not be able to explain why. Everyone learns differently. Some need to know why it is the way it is. Some take notes and write everything down. I have never been a note taker, myself. Whatever works for the individual learner.