I'm a 16-year old female runner trying to lower my 5K PR from 20:15 to sub-20:00 and 10K PR from 41:31 to sub-40:00. Right now my schedule looks like this:
I'm doing about 40-50 miles a week. As you can see I have some strength work basically everyday. I'm not too concerned about the bodyweight strength exercises, more so about the gym ones.
When I go to the gym I usually do 5 sets of 5 40kg squats and on Wednesdays and Sundays I do 47.5kg deadlifts and 15kg lunges and other core exercises. Upper body (bench press, rows etc.) on Fridays.
Is it too much? I don't have a coach and don't run for my school team so I don't really have anyone to ask for advice. I've been squatting around 3x a week for the past couple of months and managed to lower my 10K pr by a minute but I'm starting to think perhaps I should back off a bit on the weights and do some faster running.
You may want to talk with a personal trainer to structure a more specific plan so that your weight lifting is best targeting those areas most beneficial to running. In most cases, three days of quality strength work would be enough, so might also want to consider some other cross-training (swimming, cycling, a variety of other gym machines and so on). Too much "muscle bulk" will actually slow you down, and you also do not want to over-strain areas important to running performance.
I think you have a good plan to focus on intervals and tempo runs, since increasing speed is the goal. You would also be okay adding another LR to your weekly schedule to replace some of the gym sessions and better prepare for 10k events.
Wishing you all the best.