1. Many people look forward to the New Year for a new start on old habits.

[What is the meaning of 'on'? Is 'on' 'about' here?]

2. Happy New Year. Here’s to another year pretending that I like you people.
[Do we have to use 'to' in the second sentence? Does 'pretending ....' modify 'another year'?]

I think it means a new start on efforts to break old habits that one doesn't want to continue. If one has tried to quit smoking (or eating too many sweet desserts, whatever the bad habit is) and not succeeded, the New Year is a time to try again, work on it.

Thank you. Is 'on' similar to 'about'?

2-2. Happy New Year. Here’s another year pretending that I like you people.
[What about this sentence? 'to' is deleted here. Is 2-2 okay?]

2-2 is grammatically correct, but it's a rather negative wish for someone else's new year! Did you intend it to be negative?

1. In the phrase "a new start on old habits," the word "on" is used to express the idea of continuing or resuming something. In this context, it means that the arrival of the New Year provides an opportunity to begin again with old habits. It does not have the same meaning as "about" in this sentence.

To determine the meaning of a specific word or phrase, you can use a dictionary or online resources like Merriam-Webster or Oxford Dictionaries. These sources provide definitions and examples to help you understand the meaning and usage of words in different contexts.

2. In the second sentence, the word "to" is used to indicate a direction or purpose. When we say "Here's to another year pretending that I like you people," it means that the speaker is making a toast or expressing good wishes for the upcoming year.

The phrase "pretending that I like you people" acts as a modifier for "another year," expressing the manner or nature of that year. So, it modifies the noun "year" to convey that the speaker will spend the next year pretending to like the people around them. This construction adds a sarcastic or ironic tone to the sentence.

The use of "to" and "pretending" in this context is idiomatic. It is a common way to express a humorous or cynical sentiment. The construction "Here's to [something]" is often used for toasting or expressing wishes related to a specific topic or event.