Yes, this is gluten free
Gluten-free regardless of starting material, per the National Celiac Association. In North America it is made from corn.
Sugar cooked until it browns, then standardised into one of four classes — E150a to E150d — depending on whether ammonia or sulphite compounds are used to control the reaction. It is the most widely used food colouring in the world and it is what makes cola, soy sauce, gravy browning, dark bread and whisky the colour you expect them to be.
Because the specification permits a gluten grain as the starting sugar. Caramel colour can legally be made from malt syrup or starch hydrolysates derived from wheat, and people who have learned to treat "malt" as a stop word find that out and reasonably stop. The gap between what the specification permits and what manufacturers actually do is the whole answer here.
Nothing to do. This is one of the few ingredients where the answer is the same under every regulator and in every product, and the correct response to seeing it on a label is to carry on reading. If a product containing caramel colour is a problem it will be for another reason — the malt in a malt vinegar, the barley in a stout — and that other reason will be named separately.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.