Neat, I think all your fears are normal!! Firstly congratulations!!!
The way to calculate the due date is the first day of your last period. Dont' be too worried, you can have a dating scan or wait for 12 weeks and that ultrasound will tell the dates.
Also, it's up to you when to tell people. There's no gaurantee's, I told people at 4 weeks. Some choose to wait until 12 weeks, however there are no gaurantee's right up until you have bub, so I say enjoy and spread the word!! (Unless you were high risk for m/c in which case you might want to wait).
I had morning sickness from day dot, but it varies with different women, some dont' get it at all.
I didn't suck my belly in!! I felt that I shouldn't and it was kind of a relief not to!!!
good luck and have a great pregnancy xoxo