It's not that formal, but it's commonly used among friends and acquaintances. It would be better to say, 'I would like to treat you to lunch.' It means you would like to pay for someone's meal (in Australia we say 'my shout' which means 'I will pay'). Treat is pronounced like 'tree' with a T on the end.

It might mean Happy New Year!

A New Year Has Started

I'm not the kind of person who makes new year's resolutions, so I didn't even have something planned for this year. I just keep working on my old goals. I think making those resolutions is kind of pointless, if you want to do something, do it right now, not when a new year starts. Don't waste time.

Last month, I kind of allowed myself to do things that I don't usually do, such as pigging out on a lot of sweet stuff, neglecting my workout and my learning; you know, all those things that many of us do on Christmas eve. However, it's time to get back to business and say ``Hi again`` to the gym.

I had this goal that I set to myself, I said I would become fluent by the end of the past year. I think I kind of did, but I'm still practicing because I'm aiming for something more ambitious. Plus, I want to learn a new language, maybe two; I have to adjust myself to this new job that I have at a pet/stationary store, which I think is not a big deal; and learn more about history and geography, because I've always felt that I'm a bit ignorant in that regard. All I just mentioned is not something that I'm going to start this year, I will rather carry on doing it because I already started last year.

Thanks for reading and if I made a mistake please correct me.

That's the only additional correction I think you need!

The two phrases that I learned today (Two)

1.tuck into
（1）to put a child into bed and make sure that they are warm and comfortable by covering them well.
It must be tough for a mother to get used to tucking her new-born babies into bed well.
（2） eat food with enthusiasm, because the food is tasty or you are hungry.
This little boy is tucking into his tasty lunch, filled with satisfaction and joy. 

2.pledge to
He pledges to quit smoking with the witness (help) of his friends.

Witness doesn't really fit this context. Witness implies a legal or religious context usually. 

3.defer to
Most of the time, parents should defer to their children on what they like or don't like, but parents also need to make decisions for their children when they are debating.
4.self-assured
Bruce Lee is the most self-assured person who I have ever known.
5.vice versa
You are so unique for this team, no one else can replace your position, vice versa.

This sentence doesn't really make sense. A different example is: Mary likes Bob and vice versa. This means Mary likes Bob and Bob likes Mary. 

Another example: Breeze is a synonym for wind and vice versa. Breeze is a synonym for wind and wind is a synonym for breeze. 

Experience that gave me a bad mood yesterday...

Yesterday I experienced racism at the mart (I would use the word shop instead of mart because I am Australian but if you are in America mart is more appropriate).

Because I went to the mart to do my shopping and I (you don't need to say I again) tried to pay for stuff at the self-service checkout. Then a mart worker (haha, this is a funny way of saying shop assistant) came to me and said, like “I’d like to check your bag” so I showed her my bag. But she never checked other people such as  Australians. She made me freak out and I felt like telling her 'fucking racist'. I am okay that she checked my bag. Really I am sure. But I think it’s unfair. She had to check other people’s bag so as to do that to me. Thanks to her, I was in a bad mood all day.

I'm sorry this happened to you.