Is "look into one's eyes" different from "look at one's eyes"?

I've never seen "take" is followed by "-ing" form! Could you explain this sentence for me?

Sure! Here, "take" is the main verb. The direct object of "take" is "me." "Swimming" is a gerund. The form of a gerund is "verb+ing." And here, it acts as part of the object and gives more information about where one would be "taken" to. So "You" is the subject, "take" is the main verb, "me" is the direct object, and "swimming" is the gerund that provides more information and context! It means to "lead," "accompany," or "escort" someone or something to a place or activity. Ex: She took me shopping = She took me to the shops. Ex: William will take me bowling this evening.

Doesn't "private" and "personal" are basically the same word? Or do they have some significant changes?

These two words are very similar in meaning, you are correct! However, there is a difference. Personal means belonging to or affecting a particular person rather than anyone else, whereas private means belonging to one specific person or group of people only. So you can think of it as private only applying to either a group/individual vs. personal only applying to an individual. However, they are used interchangeably quite often. Ex: This is my personal workspace. Ex: I don't like to share my private life with others.

What does "umami" mean?

The origin word of "umami" is Japanese. It's used as a flavour category in food. Specifically, a flavour that is savoury or meaty. Ex: The broth has an amazing umami flavour. Ex: Wow! This meat is umami.

What does "in my disgust" mean?

"Disgust" is a reaction of repulsion due to something that is unpleasant. So in the case of the video here, "implicit in my disgust" means that he thought he was being clear on asking whether they were sleeping together due to his reaction which should have communicated his feelings of disgust. "in my disgust" is not a general expression, and it is just used here to mean "due to my disgust".

Does "crave" have a stronger meaning than "want"? Is it ok to replace "crave" with "desire"?

Yes. Most of the time, "crave" has a stronger meaning than "want." It just depends on the situation. "Crave" means to have a very strong feeling of wanting something. "Want" means to wish for a particular thing or plan of action. To answer your second question, yes, you can replace "crave" with "desire." "Desire" means to want something, especially strongly. Ex: The puppy craved attention from its mom. Ex: I really want ice cream. Ex: What he desires most is peace and quiet. Ex: I'm really craving pizza right now. Ex: What do you want to drink? Ex: Pick what you desire.