with 33/43/34/44 minor, we may choose which minor to open, we have no strict rules.
answers to 1m
inverted minor raises - but NOT in competition and NOT as passed hand. a direct minor raise denies 4 card major. after inverted minor raise, immediate 2NT or 3m from both sides shows minimal hand, NF.
jump in other minor (1C - 2D or 1D - 3C) is intermediate raise (~ 7-9 HCP), fit jump is weak (~ 3-6 HCP)
walsh style (majors first, bypassing 1D response).
subsequent actions
1m - x - 1NT shows a balanced hand, 15-17 HCP or 12-14, depending on which range 1NT opening would be. usually bypass a major (for example 1C - 1H - 1S shows an unbalanced hand, with balanced hand and 4 card spades, bid 1NT). double checkback after 1NT rebid.
1m - 1M - 2NT is either normal balanced 18-20 (may have 3 or even 4 card fit) OR strong hand with minor onesuiter (stronger than 3m). a special 3C relay is used.
1m - 1M - 4m/4M both shows a 64 hand with good minor suit (2 big honors). 4m is stronger (4 losers), 4M weaker (5 losers).
1m - x - 3NT is to play, based on solid minor