Feed dog problems are almost always solved by cleaning and oiling.
1. Unscrew the stitch plate and clean the area around feed dogs (probably race, hook and bobbin case too). Scrape each groove in the feed dog plate clean, and polish parts up if needed.
2. The feed dogs roll on a cam like part under the base. It's linked by multiple parts from the stitch length lever to the feed dogs; which means you have to pay particular attention too the oil points involving these parts. One of them is likely frozen up and needs extra attention when it comes to dissolving dried up oil and grime. The trick is to oil all parts on the machine, then move the stitch length lever to extreme posistions and run the machine for a bit between oilings. Eventually it will free up, but in stubborn cases you might need to let the oil seep in over nigh and keep up a daily oiling and test sewing routine for a while. Dirt and grime tend to loosen gradually and it takes time for fresh new oil to flush out and replace old dirt and grime.
3. Feed dogs could be lowered, it has a
screw under the base, it has two position feed dogs raised or lowered.
Best of luck with your new machine. Yours look like it's in nice condition and should shine up very well. Model 15 had a long production span, and it went through various minor chances and improvements along the way. There is an old version of model 15 with a different stitch length adjustment mechanism than yours. You have the newer with reverse. It also came as treadle, hand crank, belt driven motor and like yours a direct gear driven motor a.k.a potted motor. The subnumbers indicate these variants.