Footbridge here?
https://www.geograph.org.uk/photo/6614935

Should be historic milepost about here

Looks like a paved surface. Better tagged as cycleway?

Also phone box?

Boundary stone about here
https://www.geograph.org.uk/photo/6056242
?

Area has changed. Wait for imagery to catch up

Car park is a bit of a mess

This doesn't look right. On the ground could only see the driveway to Brundholme. Is there really a separate cycleway? There was no signage indicated designated cycle access and no indication of a PRoW on OS maps.

Path was marked as washed away in 2016, but looks to have reinstated (at least up to point surveyed). Supported by Strava heatmap.
Access is unclear - OS marks short section as "permissive", but no signs evident.

There's a strong Strava trace here correponding to a way that has been tagged as a disused footway. This is clearly not correct, even if it should be access=private.