Part 2 'Verb + like + phrase/noun' is a form in English that describes how the action is perceived. You can think of the phrase/noun as an example of how you perceive the action. It's often used to describe observations (ex. "He looks like a gymnast") or for exaggeration (ex. "The sky looks like its about to fall down"). Sometimes the comparisons are a bit abstract, so you might have to think about them until you get used to them. Ex. "This food tastes like cheese." or "This food tastes like it is cheese." - The food may or may not actually be cheese, but it tastes identical. "You eat like a pig." or "You eat like you're a pig." "Their singing sounds like a cat being tortured." or "Their singing sounds like a cat is being tortured." Note that you cannot say "This food looks like good" or "The sun looks like bright", because 'good' and 'bright' are not nouns which the food/sun can look identical to. You need to say "This food looks good"/"This food looks like it is good" or "The sun looks bright"/"The sun looks like it is bright". You can use 'feel like' similarly. Ex: "I feel like a truck ran me over." - ie. The feeling I have now and the feeling I would have if a truck ran me over are identical. Obviously this shouldn't be taken literally. This is something you'd say when you're feeling very sick, moody, tired or hungover. "I feel like tomorrow won't be a good day." - ie. You have a (emotional) feeling that tomorrow won't be a good day.

To feel something is to feel it emotionally. It can refer to the sensation of touch. There are five types of senses (that humans have): touch, sight, hearing, smell and taste To sense something is to perceive it with these senses. 'To sense' is often used metaphorically, usually to describe something that you know intuitively. There are two main ways 'feel like' is used. The most common one is just a common form in English, and the other is specific to 'feel like'. I'll quickly describe the latter first: 'Look like' can be used with the continuous tense, where it essentially means "want to". You can see this in Lydia's example: "I feel like going to the park for a run" means "I want to go to the park for a run". I can't think of any other verb which can be used like this. Most of the time, 'verb + like' must be used with a noun or phrase. My reply has to be less than 2000 characters, so I'll put the rest in another answer.

I will let someone else answer the rest, but I will just add something: "Feel like" is used also for a case like this: "I feel like going to the park for a run" that is to say, I have the desire to do something, I feel like doing it. (I am not sure why we say that, perhaps it comes from the idea that I sense/feel within me that if I do it I will feel better, or it will be for good).