Growing these plants in the same container would be fine if it is big enough. There wouldn't be any transference of toxicity.
Ipomoea genus includes sweet potatoes. What kind are you considering? The gorgeous I. alba in your pic? I've not seen discussions about it being toxic but anything not widely considered edible should be assumed to be terrible-tasting at best, indigestible or dangerous to some degree at worst. Using sweet potato & "regular" potatoes as example, the tubers are edible but the leaves should not be eaten. Many plants are that way - parts are edible but the other parts should not be eaten.
Squirrels can be kept out of pots by covering the soil surface with something sharp, like toothpicks, plastic forks with the handle in the soil & tines up, broken twigs - whatever's handy that would make it uncomfortable for a squirrel to get in there to dig around. It would be best to use something that won't inhibit the exchange of moisture & air, like covering the soil with rocks.
