If all else fails, call FileMaker tech support. They should be able to walk you through the various options in a way that takes much longer to do in this forum.
I could be wrong, but I don't think they'd try to charge your for this--especially if you explain you are evaluating the software for possible purchase.
I'll do that!
You probably need to set up your router to forward to the specific computer that hosts FM. You probably will also need to assign it the same IP (static LAN IP). Lastly, you will need to make sure that the port is being forwarded properly from your modem to your wireless router.
It doesn't solve your connection problem, but in terms of your assessment of Filemaker, connecting remotely, either using IWP or from the FM client, rest assured it is done every day and works really well. This will just an issue with your router set-up.
Given that you have two possible port blocking apps on your Windows laptop, can you try some other computer outside your local are network?
Your cable or dsl modem has a port that your router is plugged into, plugging the FMP host directly into the modem sometimes will get around the router's possible misconfiguration.
Forward only the port needed - 591 is reserved for FMP IWP
Using Port 80 may be worth trying, less likely to be blocked by Windows security (Proxy server settings can also interfere)
After making unsuccessful changes to your router resetting it to factory defaults and setting the port forward again may help.
Reset it to factory defaults - there is a tiny recessed button on the back to do this.
Your Local IP address for the FMP hosting computer may change after the reset NOTE it.
IWP access across Internet
FMP10 IWP Setup PDF
Testing your IWP setup.
Open the database, make sure that IWP is turned on and note the IWP PORT setting
[ ] My webIPaddress is ___ ___ ___ ___ http://whatismyipaddress.com
[ ] My FMP hosting computer's localIPaddress is ___ ___ ___ ___ shown in FMP IWP setup
[ ] My database is open
[ ] My database is set to IWP Port ______ shown in FMP IWP setup
 At the computer that is hosting the database, open browser and enter http://127.0.0.1:591 or http://127.0.0.1:591/fmi/iwp (or http://localhost:591/fmi/iwp)
This is the self IP address of any computer - 127.0.0.1 is the local IP address of the computer you are typing on.
If the database does not open, the IWP settings in Filemaker or the database are incorrect.
This should work if the first test works.
 At a computer on another network, open browser and enter http://fmphostwebIPAddress:591/fmi/iwp
In your case it would be [188.8.131.52:591/fmi/iwp]
If the first two worked and this does not, the portforwarding on the router or firewall settings are incorrect.