Yeah you should rarely, if ever, plan on adding more than 10% in either distance or speed per week as a general rule.
More to the point of your question is whether you want to increase aerobic speed (how fast can you run 10k) or burst speed (how fast can you run < 1k).
If the latter, then yes, bodyweight exercises like squats, one-legged squats, box jumps, dead lifts (maybe with slightly more than body weight), etc can definitely help. Running stairs, hills, and/or intervals will also help here.
If you want to increase aerobic speed then those same exercises can help, but not nearly as much as building your aerobic base. There are lots of theories on base building, but the basis of most of them is a lot of steady mileage below your anaerobic threshold. A good way of determining this is your max heart rate (usually 180-200) minus your age. This keeps you much more in fat-burning mode than sugar/glycogen burning mode.
If you train at this level, you will eventually (60 days? 90 days?) notice that you can run for the same amount of time and a faster pace at the same heart rate. This is because you will have increased your ability to convert fat to fuel. This will increase your 10k speed, as well as increase the distance you can run at the same pace.
Note: If you train at a given heart rate for a given duration, it will mostly likely result in having to slow down, sometimes significantly, for a while as most of us run with a higher than mostly aerobic heart rate. But over time, your long-distance speed will increase.