A softphone is the general term used to describe a VoIP phone connection where software that is installed, is used to create a phone connection on a computer. The PC acts as the phone with a virtual phone displayed on the screen. A head set is generally needed for good conversations, one with both a microphone and head speakers. Although softphones or a PC application phone are liked and used by many people, they have not as of yet taken off in the business environment, which still prefer more traditional phones.
Yes, you can work on the computer while on the VoIP phone. They should not conflict with each other.
A Hosted PBX or an Internet Business Phone System is a VoIP business phone system where the “PBX Hardware” resides at the provider. Usually rich in features, a hosted PBX can save significant upfront hardware charges because the PBX software/hardware sits remotely at the provider’s facility and connection is made through the Internet.