Bags: (assuming on same ticket): transferred straight through.
Hand luggage: bmi policy apples - as it is still operated by bmi under a BD flight number (931). bmi's policy in Y is one rollaboard (yours is fine) and one personal item. You must be able to lift them both into the overhead locked unaided, that is the real weight limit. Of course, to be considered a personal item, you can't put a ton of stuff in it!
You can have your bags gate-checked - this happens quite frequently on midhauls, and as you pass the boarding pass/documents check at certain T1 gates before being seated in the holding pen (from past experience these gates are used when they are almost certain of having to do that). They'll just give you a baggage tag (and make sure it's for EVN and not IKA where the flight continues!)
Lounge access - I'm 99% sure you already asked this question before? In any case, in Y, unless BA/BD Silver/Gold, then no, as it's a bmi flight.
Have a nice trip!