Running Filemaker of my Macbook Pro, loaded Filerserver also on my Macvook pro.
This is a bit of a worry. You don't need a file server to host a FileMaker database.... you need either FIleMaker Pro or FIleMaker Server. If you share a file on a FileServer you will damage the file.
If your database is open on your 'server' (ie your MacBook Pro) and you open up FileMaker GO on your iPad you can enter the local address of your MacBook and access the database. WHat you change on your ipad should immediately update on the hosted database.
If you want to access the database from the internet, you must have port forwarding set up on your router to point calls for FileMaker on port 5003 to your MacBook.
It would seem more likely, and polite, to assume a fat fingered attempt to type filemaker server?
Seems like Lyndsay's advice was eminently polite, not to mention a well-articulated description of a critical point. You might be correct, of course, that the OP actually did mean FileMaker Server, in which case s/he can chime back in to clarify. (I actually read it the same way as Lyndsay; perhaps because I've seen people try and run FileMaker from a file server, and have known IT folks who insist that that's OK. Yikes!)
OP - by way of (brief ;-) reply to your other question, yes data hosted on FileMaker Server can be accessed via the web, using either of two supported tecthonologies: custom web publishing and instant web publishing. Entire books could be written about each of those, but if, as you explore them, you have specific questions, this forum will be a great place to which to turn.