What is “virgin Cuba Libres”? Is it a drink name?

Should we use "to" when recommending something? So should this sentence be "Do you recommend people TO eat Durian"?

No, the word "to" isn't really necessary when recommending something. You can add "to" in the sentence, but it's not always needed. It really just depends on the structure of the sentence. Here are some examples of recommending others to something with and without the word "to." Ex: I recommend that you eat pineapple. Ex: It is recommended that you go to college for certain careers. Ex: Do you recommend that others try eating more vegetables?

What's the difference between "start", "begin" and "commence"? For example, I've often seen the antagonist of the movies saying "commence the attack" instead of saying "start the attack", however it's hard to tell the difference.

In this context, they pretty much mean the same thing! What's different here is the tone. "Commence" has more of an official tone than "start". I'd also say "start" has a few more meanings than the other two words. "Commence" and "begin", both mean for an event or something to begin. "Start" does have the same meaning as begin in some contexts! However, it also means for something to happen or exist, the beginning of something, or a sudden movement. Ex: Jill tried one more time to start the fire, and it worked. Ex: The race is going to begin at five am. Ex: Let me tell you a story, It all started when I was ten years old, and I baked my first cake. Ex: Commence lift-off in: Three. Two. One. Lift-off!

Isn’t this sentence necessary "the" before "easy way"?

If you're regarding listening, I'm afraid there is no 'the' before 'easy way'. Regarding grammatically, only using 'the' before easy way is grammatically correct, but phrases like 'what the easy way' feels very awkward. Using 'What easy way' or 'What is the easy way' would be more natural.

What does “be about to” mean?

"Be about to" means to start to do something; to start an action. Here are a couple of examples: Ex: I was about to bake a cake until my children interrupted me. Ex: They were about to go but then they got a flat tire.

What does “be in one’s feelings” mean?

To "be in one's feelings" is not a general expression but in this case it is used to refer to being very emotional or sad. However, it is more common to say "feeling emotional".