Yes, and yes.
When you get FiOS, Verizon installs a fiber optic connection to your house, your old copper connection to the Central Office is disconnected. That new single fiber is used to transmit your voice (phone) traffic, internet traffic, and TV signals (if you eventually get TV). It uses different light frequencies for each type of traffic so they do not interfere with each other.
The fiber is connected to a box at your house called the ONT (Optical Network Terminal). This box converts the light signals to electrical signals (and vice versa). Your existing house phone wiring is connected to the ONT for telephone service. A coax cable is connected to the ONT for internet traffic, and is connected to a Verizon-provided wireless router, which is where you connect your computer(s), either wired or wireless.
Everything can be used at the same time. And I have never seen any effect on one service by using another service (phone, TV, or internet).
Here is a link to the Verizon website that has a reasonably good description of the FiOS service:
http://www22.verizon.com/content/consumerfios/about+fiostv/about+fios.htmYou will be simply amazed at the speed and reliability of FiOS, go for it. And just in case you are worried, I am not a Verizon employee, I don't own any Verizon stock, I have just had FiOS phone, internet, and TV service for two years, and just signed up for a new two-year contract. And I love it, compared to the cable service I previously had!