1. No, a cake doesn't have to be made of wheat flour and it doesn't have to be a dessert. Loosely speaking, a cake can be anything that it is made of ingredients bound together into solid mass. For example, a 'fishcake' is a dish which isn't baked, isn't sweet, and doesn't usually contain flour.
2. There are many different types of sausages that can be served in different ways. A typical cooked breakfast in the UK, for example, includes large thick brownish sausages, eaten with a fork and knife, on a plate alongside bacon, eggs and so on.
A hot dog is a 'frankfurter' style sausage. These are long and thin in shape, fairly soft, and pink in colour, mainly because they are highly processed and often contain colouring and flavouring. They are eaten in a soft bread roll, usually with ketchup and/or mustard. Hot dogs are always held in the hand.