Definitely illegal
1.
Black has 9 pawns
2.
Rook a1 could be legal in isolation as a promoted pawn, but in light of #1, I'm declaring it illegal
3.
Bishop b1 cannot get there
4.
Both white bishops are on white, white has 8 pawns, one bishop is illegal
5.
Both kings are in check
6.
Black king is in illegal double check, could not be discovered by legal movement of either offending piece
7.
Black rook starting h8 could not have legally escaped, due to number of remaining black pawns, absence of rook considered illegal
8.
White pawns are at least 3 places off home columns, black still has 16 pieces, though missing a knight, at least two illegal places off home
9.
Pawn f7 is illegal, cannot have captured the required 2 pieces to return to home column behind black pawn as black not missing enough pieces
10.
Even assuming pawn g3 to be the interloper, black pawns are a minimum of 4 places off home column, white is missing 4 pieces, but rook a1 could only have been captured by a knight or queen, at least one illegal place off home
Not illegal but might look it
1.
Bishop f3 check could be discovered by movement of knight h4 from g2, otherwise it's really hard to get into that position
- This ties into illegal #10
Assuming bishop b1 to have been placed there at the start of the game, white rook starting a1 could not have legally escaped, but could have been captured by a knight or queen. Black bishop could not have been used.