In this situation, after halting and making sure that no train is approaching, do you have the right to proceed without waiting for permission from an authorised individual?

In the photo you are approaching a level crossing with the barriers up; on the right there is sign B-32 with the words "Rogatka uszkodzona" (barrier out of order). After stopping and making sure that no train is approaching, you are not entitled to move off without the permission of an authorised person. The answer is: no.

The Regulation on road signs and signals states that sign B-32, including the version with the words "Rogatka uszkodzona", means an obligation to stop, and you may continue only with the permission of an authorised person or after a signal allowing you to go has been given. The difference from the ordinary sign B-20 is fundamental: at B-20 you decide yourself when to move off, and at B-32 the decision belongs to someone else - a railway employee, a crossing keeper or a signal. The reason: when the barrier is out of order, traffic at the level crossing is directed by a railway employee, who is in contact with the traffic controller and knows whether a train is coming; your own "making sure" from the car is much less reliable. So you wait until this person gives you a sign, even if the track seems to be empty. If there is no one there and no signal, you do not enter - you call the number from the yellow sticker at the level crossing.

Legal basis: § 26 para. 1 and 2 of the Regulation on road signs and signals; Art. 28 para. 1 of the Road Traffic Act (Prawo o ruchu drogowym)