STIR together the olive oil and garlic, in a medium mixing bowl. Add the squid and toss. Set aside for at least 30 minutes or refrigerate for up to 1 day.
PREPARE a medium-hot fire in a charcoal grill or heat a gas grill to medium-high heat. When ready to cook the squid, season it with salt. Grill the squid, turning occasionally, until it's lightly charred and cooked through, 5 to 7 minutes for the bodies and 3 to 4 minutes for the tentacles. Transfer the squid to a cutting board and cut the bodies into ½-inch rings.
TOSS the squid with the vinegar, lime juice and zest. Add the shallots, cherry tomatoes, fresh chile, cilantro, purslane, basil and peanuts, and toss. Taste and adjust seasoning with salt, chile and lime juice if needed. Serve.