Or if FAR meets NEAR and crosses over, at what distance does this happen?

Just curious if I need FAR Labels.
Or can I still get smoked if a bandits Label is considered FAR?

Near labels max = 20 miles

Far labels min = 20 miles

Don't mind posting this for you, but I had to run a mission to find out. I think you would have learned more by running one yourself. It may be in the manual.

Anything inside the bubble is considered "near", anything outside is considered "far". I have no idea how far the "far" labels go.

20 miles is the near/far boundary for A/A only. This is approximately the size of the A/A bubble.

5 miles is the near/far boundary for A/G.

Can you be killed by something which is "far". Yes. BVR missile launches do happen and bandits will fire from outside the bubble at things which are inside the bubble.
Conversely, can things inside the bubble fire at things outside it? It appears not. Only you, or your wingmen if you order them, can fire at bandits outside the bubble.
Any other allied flight in your bubble appear not to be able to see out. If there are allied aircraft on the fringe of your bubble, they may have bandits at only 5 miles but if these are outside "your" bubble, they don't seem to see them. They get shot without shooting back!