Is it possible to cross the Blaine-White Rock border on foot or bicycle? And are there tolls in either direction?
There is a sidewalk that runs through the Peace Arch Park, next to the northbound lanes, between the Canadian border checkpoint and the US border checkpoint. As a pedestrian, you should cross into the park and follow the sidewalk across the border and to the checkpoint.
Bicycles can use the roadway to pass by all the cars, but in both directions you will also want to get onto the sidewalk where it crosses the road and go to the pedestrian/bicycle area of the border checkpoint. On both sides, it's at the far left of the booths.
After crossing, on the US side you can continue following the sidewalk to Peace Portal Drive. On the Canadian side you should take the first left onto Beach Road. It is a dead end for cars, but a pedestrian/cycle path connects it to Marine Drive/8th Ave.
There are no tolls of any sort at this crossing.
I don't know about tolls.
In normal circumstances, there are no restrictions for people crossing on foot or on bike (you need to have valid ID).
But these days, crossing between Canada and USA is restricted to essential workers (and freight).
Canada version: https://www.cbsa-asfc.gc.ca/menu-eng.html
This video is in Niagara, I assume you can do the same in BC. https://www.youtube.com/watch?v=P-UsZTlF7NA