Calls often drop now. and I often get a banner across the top that reads,"no internet connection available".
It is updating a PRL (preferred roaming list), which some claim has helped improve problems like the ones you're having.
Here's the wikipedia page on Verizon's PRL:
Preferred Roaming List - Wikipedia, the free encyclopedia
Probably not, but you might as well give it a try. Verizon offers a femtocell (Femtocells are compact wireless base stations that boost cellular signals indoors to provide enhanced coverage up to 5,000 square feet), which is supposed to be like having a cell tower in your house. If I remember correctly, they are expensive and probably not worth it.