Another option to make 45 and 50mm chain line components, or road shifters and mtn bike front derailleurs, play well together is by using a Jtek Shiftmate.
Shiftmate 7 mixes Shimano & Campagnolo triple road shifters with mountain bike front derailleurs
I recently did a drop bar conversion on a Trek 7.5FX hybrid with a trekking/mtn bike crank. The Shiftmate 7 makes Ultegra 3x9 shifters play well with the mtn Deore front derailleur. As mentioned(if you're converting to drop bars and road shifters), Travel agents will be needed to make the current brakes compatible, or switch to a set of cantilever brakes.
All that said, you have mtn bike shifters on their currently. I too think your cables are really tight. I'd guess you mounted the trekking bars using the cables from the flat bar you removed and tried to make them work without replacing with new, properly sized, cables and housings.
As for the wheels..yes, no, maybe. You haven't shown any good pics of the wheels, hubs..etc, so it's hard to say what shape they're in. What are they? At a minimum, I'd go through the hub bearings by cleaning up the races and cones and (properly) reassemble them with fresh grease(Park Tool has all kinds of videos to show how to do hub, derailleur, shifter, chain..etc.. maintenance). Then go through the spokes to check the spoke tensions, true the wheels etc..