Filler cell won't fix the metal density, but as already explain, fix nwell.
The filler cell is only required between std cell, not mandatory for start row to the first std cell ( same idea to the end of the row).
And the filler cell is not needed to finish the power std cell connection.
Filler cell don't impact the timing because the filler cells should be added before the routing.
capacitance filler cell could impact the timing because the routing usage is not null as the filler cell.
Filler cells are used for well continuity.
Imagine there are two standard cells with some space left in between them. so there is a discontinuity in the NWELL (for a NWELL bulk process) in this empty space, which affects your lithography step. In order avoid this, designer should make sure that there is no discontinuity in the NWELL by placing a filler cell.(Which fills the NWELL)
Also, there could be some mechanical stress by the layers present above the vacant space
Filler Cells are used to avoid the Base Layer ( Nwell, PPlus, NPlus ).
The flow is,
* Insert the Filler cells once you're done with the Routing & Optimization
* Then dump the DEF from implementation tool.
* Parasitic Extraction from QRC/Star-RC
* Timing Analysis using PT
* If Timing Violations are there, then go back to the Implementation tool.
* Delete all the filler cells & fix the timing.
the same procedure continues till you close the timing.