For the stretching, pick up Tom Kurz' Scientific Stretching. It addresses your questions. Three times a day may or may not be excessive; it depends on how you do it. You might get more mileage out of doing yoga a few times a week and developing a home routine.
Running is not strength training unless it is sprints. 800 meters is way too long for strength work; if you want strength do deadlifts and squats and pull-ups and dips. I find Romanian deadlifts quite useful for simultaneously strengthening and stretching the hamstrings, for instance.
Make sure you do plenty of counter-movements to the BJJ work: opening the hips and shoulders to reverse the curled-up posture common for most groundwork. This article is a good overview:
When you’re in guard, attacking from the side mount, back and many of the other positions, your body is in a contracted state.
The upper back is often rounded as you are holding onto your opponent, the hip flexors and psoas are usually tightened because the knees are tucked up towards the chest, and as for the neck and shoulders – well if you’ve been training for any length of time you’ll know exactly what I’m talking about.This excessive contraction is even more pronouced in the primary defensive postures, like the turtle postion. (Interestingly, the ageing process is also characterised by contraction – this is why old people start to hunch over.)
Regular practise of the various asanas and vinyasas is the best remedy I’ve found for this imbalanced state, due to their twofold effect of lengthening and opening the body.