I had DCs 4 & 5 at 40 and 43
I didn't have any tests apart from the routine bloods.
I had no problems at all during pregnancy.
I had two HBs with no PPH
MW for DC5 got a bit weird right at the end and tried to talk me out of a HB due to my risk of PPH but I took advice from several sources and it seemed she was over reacting. She said I was multi gravida (I wasn't, DC5 was my 4th birth as one mine is adopted), I hadn't had any PPH or excess bleeding with any of my births and I had no other risk factors.
I later found out she had only been to one HB as a student and was panicking a bit 
If you have had a previous PPH afaik you are at increased risk of another.
My care was all community MW led. I only went to the hospital for my dating and anomaly scans.
I had no extra care during my pregnancies. In fact I had far fewer appointments due to things having changed so much in antenatal care between having DCs 1 & 2.
Back in those days you went to the hospital every four weeks.
I find a concentration on the negatives of older mothers. This is all based on statistical information (which ignores the individual experience) and mostly around the risk of giving birth to a child with a disability.
I find that depressing and TBH it got me down a bit when I was pregnant. At time I felt like a bit of a freak and like I was doing something irresponsible.
But that is the downside of the internet.
The upside is that you find lots of women who say 'meh, I had a baby when I was 45 and it was a breeze'
Good luck.