BI was removed cause it was old technology, it had almost no new features and mostly because it was all over the blender’s code and that even disturb adding options unrelated to BI.
If it weren’t disturbing blender development it probably woudn’t be removed.
Is EEVEE replacement of Cycles or Internal?
Lets use analogy:
Well if we wanna drive a nail, but we dont have a hammer, however we have a shovel (or screwdriver) so to drive it we just use what we got. Then we got finally hammer, is the hammer replacement of shovel?
Yes and not. We can finally use tool that is meant for a job, but we won’t use hammer to dig a pit. Hammer will replace shovel with the jobs for hammer, but it wont replace it completely since old tool is still superior in job that it was mean to do (digging).
Interlal is fast offline rendering
Cycles is realistic offline rendering
EEVEE is meant to be realtime rendering. It can get functions that are only meant for offline renders, like UnrealEngine have options only for Cinematics. So in further feature it actually can replace Internal since it is gone.
In the end all those engines produce images, so theoretically they share their purpose, but they are more specialized with task, cause we don’t have enough compute power yet to produce fast enought images with some king of raytracings.