1. It depends! Yoghurt is usually sold in pots or cartons. So if he takes the lid off and eats it straight from the pot or carton, you could say "He usually eats a pot/carton of yoghurt for breakfast". If he buys a large pot of yoghurt and puts a portion of it into another receptacle before he eats it, then it could be anything - a bowl of yoghurt or a dish of yoghurt, for example. 'Cup' is a little strange, because we usually drink out of cups. Cups are generally for liquid e.g. a cup of coffee or tea. We pick up the cup and put it straight to our mouths. Semi-liquid foods such as yoghurt which we 'eat' rather than 'drink' are usually served in bowls, and we eat them using spoons. It's a strange question, but I'd choose 'pot', based on the word 'eat'. You eat yoghurt out of a pot but drink it from a cup. 2. I've no idea! You can cook carrots any way you want. Boiling (in a pan of boiling water) or steaming (over a pan of boiling water) are more common than roasting (in a hot oven tray with oil). Perhaps 'roasting' because there's no water involved? Or 'roasting' because it's done inside the oven rather than on top of a stove? I suspect that 'roasting' is the answer because the writer doesn't think that this is a normal way to cook carrots, but it's a pretty silly question. NB Saheed, the first person to answer this question, attracted downvotes : but he has a point. Different cultures have different traditions around food and drink. Presumably, in Saheed's culture, it is normal to drink yoghurt rather than eat it and to eat carrots raw than cooked. This shows what a poorly conceived question it is - the question seems to be testing culture rather than language.

For your first question, I'm not sure if you want the question mark to turn the statement into a question, or if you simply put it there to simply mark your own question. Therefore, I will give two examples. 1.) He usually eats a cup of yoghurt for breakfast. 2.) Does he usually eat a cup of yoghurt for breakfast? 3.) Roasted, boiled, and steamed are all valid ways to cook carrots, and don't sound unusual in English.

1) Yoghurt is not eaten but drank i.e no option is correct 2) Carrot is not processed before eating

We don't roast carrots at least here in china, but wether it's odd or not may vary from area to area. I would use cup or carton for yoghurt.