How do implied tag values work?

I'm trying to understand how implied tags work. I've been doing some Googling and searching around on the OSM wiki, but haven't clearly understood them.

• If I tag a way highway=footway, then (by this list), a routing engine will assume that this path cannot be used for motor vehicles (as if the way was tagged motor_vehicle=no) - depending on the country. Is this correct? Is this implied tagging implemented in each routing engine separately, or is it a built-in feature of the OSM database (i.e. is there a "master" list)?
• The implied access tags for highway tags seems to be reasonably well documented, but other tags (notably barriers) seem to have implied tags as well. For example, barrier=bollard (according to the wiki) implies foot=yes and bicycle=yes. This documented on the wiki page for that specific tag - is there a central list of these implied tags? And, like above, I take it these are implemented at the behest of every routing engine programmer?
• Can I "override" an implied tag, or is this a bad idea? For example, explicitly tagging foot=no on a highway=path if (by sign) pedestrians are not allowed on that path (even though, by default, highway=path implies foot=yes)?
• Are there other kinds of implied tags, other than access tags?

The reason I stumbled across this is that I do a lot of bicycle-related tagging, and I'm perenially checking the wiki to make sure that the features I'm tagging (based on what I see on the ground) don't by accident imply access tags that would cause routers to route i.A. bicycle traffic a different way.