Can the steamer under repair be identified?

Interesting - the ship and the photo.
built 1935 Svendborg Skibsvaerft (Yd 35)
100grt 67nrt 154dwt, 81.4 x 21.6 x 7.4 feet
M 117bhp

Many thanks for detailed information.
For my side, I can add that I bought the photo from a dealer, who, as far as I understand, bought it among other antiques in Germany.
According to him, the photo was in a frame under glass, but I got one photo.

https://www.roennebyarkiv.com/merkur-mgalease.html

Rønne City Archive has obtained this photo: It was taken in connection with stack draining at Svendborg Shipyard in 1935 by M/galeas Merkur. Belonged to A/S Paketrederiet Merkur, Rønne. Managing owner was procurator Ludvig Johannes Hansen.
The persons are unknown - apart from three: second top row on the left (with cigar in hand) shipbroker L. Skovgaard, just below him with glasses and smoking a cigar, grosses L. Johs. Hansen.
About Merkur in Rønne Havn HERE.
Front far right, with handkerchief in breast pocket, captain Aage Hintze.

The two ship images show the launch of Merkur in Svendborg Harbour.

In May 1941, Merkur was taken over by captain Chr. Petersen and the same month it was named Fortuna. In January 1942 it was sold to Hellerup and named Mary Bee. Later it was called Oraplana of Frederikshavn, but disappeared on a voyage to Copenhagen on 27 February 1945. Six men perished. (Information from Erik Pedersen: With sail, steam and engine and family for the first owner, Jens Hansen.)