Does the first sign you see here tell you to drive with a speed of up to 50 km/h?

In the video you are driving along a road outside town and pass a green board with the place name "Majdan Nowy" - sign E-17a; in the distance you can see sign B-2 at a side road. The nearest visible sign does not require you to drive at up to 50 km/h. The answer is: no.

The Regulation on road signs and signals states that sign E-17a "town" (place name sign) only marks the entrance to a town or village and is for information only; the 50 km/h limit is introduced only by the white board D-42 "built-up area" with a silhouette of buildings. The Road Traffic Act links the speed of 50 km/h to a built-up area, not to the administrative boundary of a village. A green board without D-42 means that 90 km/h still applies, unless there is another speed limit sign. Even so, among the buildings you slow down out of common sense, because there are exits from properties and pedestrians on the shoulder.

Legal basis: § 66 para. 1 and § 58 para. 3 of the Regulation on road signs and signals; Art. 20 para. 1 and para. 3 point 1 letter d of the Road Traffic Act (Prawo o ruchu drogowym)