The tattoos on your belly will probably stretch - they won't look the same afterwards (a friend of mine has one next to her belly button and it doesn't look anywhere near the same) however I have one on my side/ribs and that's been fine.
You MAY not get stretch marks at all - not everyone gets them - you just have to see. I didn't with my first pregnancy.
Have you seen your midwife yet for your booking in appointment? They take bloods, check a wee sample and give you information. At the 12 week scan if you choose to have the downs syndrome testing they will also take a blood test, your weight and height and during the scan they will need to take a specific measurement of the fluid behind baby's neck - but that's all done with the scanner.
Your due date can change at your 12 week scan, as they measure baby and potentially change the dates on that but again it depends. For my first pregnancy it didn't change at all, this one I was over a week further on!
And generally people find the second trimester the easiest as a lot of the symptoms from early on (sickness, tiredness, bloating) has passed and you start to look pregnant but feel fine, and then in the third trimester is when you get uncomfortable and then start to get back a load of symptoms and things get more difficult. I'm 31 weeks now and just starting to struggle with bending and getting tired again (but then I'm also running around after a toddler this time!)
Hope that helps!