Standarization of a normal distribution

Hi team,

Can you explain a little bit in detail about the concept of standarisation of the normal distribution? I seem to be able to get it but its just not fully clear. The (0,1) is making me a little confused. Some practical detailed example would be really helpful.

Also, one more question with regards to Hypothesis testing. I have learned this concept previously too. To simplify the difference between one tailed and two tailed tests, can I say that if we have a >=,< or <=,> question to be a one tailed tests and a =,<> or <>,= to be a two tailed test. I think that is how I learnt it, but a confirmation would really satisfy me.

Thank you so much once again and god bless you.
Best,
Priyen