They also did some re-set from their side: "we break the lease that your router is holding and reboot your network terminal to get you a new address on our network" - did not help.
I and my son ran the same test using our laptops from two other houses in our area and results showed the excelent and fast big files uploading and sending via e-mail. See detailed report in my prof. blog :
(BTW I ran ping report also and saw the same sporadic time-outs, so it's not a problem.)
Now I am sure there is no problem with my laptop and the FiOS in our neighborhood is OK.
The problem is around my house. I am sending this report to Verizon support. Also I plan to call them tomorrow. We will see how they help me.