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1.)You certainly can perform these mobilizations during rest periods in place or in addition to other methods. I’m a big fan of assessing via the test/retest model where you mobilize in the rest period and assess if it improves your positions/mechanics. For example if you are doing pistol squats and in between sets mobilize the ankle see if it helps you better access that shape.
2.)TRS exercises should get you far in accessing the splits and straddle. You can use the TRS exercises to help open up the adductors and hips. Here are a few mobilizations to help you access those shapes: