As I understand, each virus type can enter a particular cell type. For example HIV can enter CD4 & CD8 cells, while HBV can enter liver cells, some other viruses can enter other cell types like brain cells and cause brain diseases.
I don't know if there is any "universal" virus that really gets into every cell type, but lentiviruses come pretty close. Lentiviral transfection vectors have been developed for a wide range of human (or mammalian) cell types, including immune cells and terminally differentiated cell types such as neurons and skeletal muscle.
But these are of course experimentally modified viruses that have been optimized in various ways for transfection; typically, the naturally occurring virus is much less efficient. I would guess it's unlikely that a natural virus can enter any (human) cell type, because this capability would be expensive for the virus to maintain, and there is probably little pressure to do so --- as long as the virus has a working route of transmission, via the airways for example, there is probably little benefit in being able to transfect other tissues.
Unlikely. There are 2 ways for viruses to enter cells - mimic something the cell normally uses and trick the cell into "eating" the virus, or grabbing onto a structure on the cell membrane and forcing its way in. Either way, it's largely dependent on the target cell
Different cell types can have vastly different surface structures and receptors. Viruses that already thrive on infecting a specific type of cell have no need to develop the ability to infect other types of cells.
A virus that could enter every type of cell would look like a completely unfolded Swiss Army knife, requiring latches and grapples for each type of cell. The latches and grapples could interfere with each other, the end result being a virus that's ineffective at infecting any cell. This would actually discourage viral mutation for such multi-infection (as an intermediate form with new cell adapters could decrease its fitness on its main cell targets)
