I think your situation is very peculiar and the best thing to do is getting a safe and sure advice (i.e. not here

First of all, this is Kela website's section for pregnancyand there you'll find all information about maternal and parental leave. There's also a way of calculating the allowance but it's only in Finnish/Swedish.
About your contract, I think it depends. I have a fixed term contract as well and by asking around I heard different stories: some told me that my employee had to "move" the end of the contract by law, some other people told it wasn't true... I am currently waiting for a sure reply by the human resources office of my workplace. I suggest you to ask to yours as well or, if there isn't any, you may take a copy of your contract and exploit thefree-of-charge legal advice available in many places in Finland. In alternative, go to Kela bringing a copy of your contract and ask them.
Another suggestion: I think you could do everything through Neuvola, you do not need any extra ultrasound or visit from private doctors. Finland has an excellent public health service especially for pregnancy. You'll get 2 free-of-charge ultrasound examinations during pregnancy and a midwife will visit you regularly.
I'm now 7 month pregnant, so if you need help or suggestions feel free to contact me on private message.
Good luck for your pregnancy!
Paola