Answering an invitation from my friend, Petra place a comma when you introduce someone

Hi, Petra! You do not know how absurdly happy I am with your invitation. I do not have many friends and generally I do not receive many invitations for social events. This week I am really swamped by a lot of chores, but next weekend I will be totally free. So I think that next Saturday would be a good day for our meeting if it works for you. What do you think about cooking lunch together? My favourite food is lasagna. I love the pasta intermingled with slices of melted cheese. Should I mention the red sauce and its flavour? Simply delicious! Maybe your parents could join us for lunch. But you decide about it, okay? We will be able to stay together all day long, but I have an engagement with the church community on Sunday morning. Thus, considering that I live far from your house, I think that I may start going home at 23:00 p.m; otherwise, I will miss (we say "miss" instead of "lose") the last bus that leaves from your neighborhood to mine

Very good job!  I just made some things sound a bit more colloquial and less formal.