If you are new on strength stuff, I would recommend doing only body weight circuit training first 8-12 weeks or longer. You could include the planks into the circuit training sessions. Just don´t try to hold the plank X minutes, stop before your form breaks down. Keep your elbows wide enough, don´t hang on your shoulders, engage the lats, keep the neck straight. Don´t overuse your hips (butt too up), you´re not trying to strengthen/tighten the hip flexors and possibly create a pelvic tilt, you need to fully use the core. Stop if your butt/hip area starts to go down.
But I think that doing planks 4 x in a week could be too much for your rotartor cuff in your shoulder area. Your arms and the tiny balancing muscles and joints in your shoulders and lats probably fatigues first --> form breaks down. You can work the core even completely without doing a single plank, i.e. one leg exercises will activate the core and other balancing muscles effectively. Hill sprints, and normal sprints will make the core stronger in a more running spesific way. Although planks are very effective also for your back, but don´t overdo it. You can strengthen the back too by many other exercises than by planks.
In general strenght training you need multiple different exercises (about 10-12) in order to built a balanced body that doesn´t break down when you move towards weights, more spesific movements, or doing more planks.
I suggest to save more energy towards running. You would really benefit from a strength training expert who knows the right techniques.