Honestly, I don't like to meeting new people. Honestly, I don't like meeting new people.

Original is correct, though this sounds a little more natural to me.

It's always difficult to meeting new people because there are many things to consider when I speak with them. It's always difficult meeting new people because there are many things to consider when I speak with them.

I think "meeting new people" is more natural.

It's always difficult to meeting new people because there are so many things to consider when I speak with them. It's always difficult meeting new people because there are so many things to consider when I speak with them.

I don't know enough about their preferences, privacy and or thoughts, so I always have to be careful. I don't know enough about their preferences or thoughts, so I always have to be careful.

"privacy" doesn't really fit in this list. Maybe "private thoughts"?

I don't know enough about their preferences, privacy andbackground or thoughts, so I always have to be careful. I don't know enough about their preferences, background or thoughts, so I always have to be careful.

You mentioned in a reply to a previous correction that "background" was what you meant here, and I think I agree. Otherwise, I would have had no idea what you meant by "privacy".

I don't know enough about their preferences, privacy and thoughts, so I always have to be careful. I don't know enough about their preferences, privacy and thoughts, so I always have to be careful.

Not too sure what is meant by privacy here.

It consumes a lot of my energy. It consumes a lot of my energy.

When I meet people I know well, I can speak in an easy moodeasily. When I meet people I know well, I can speak easily.

"speak in a relaxed mood" would also work.

When I meet people I know well, I can speak in an easy moodcasually and freely. When I meet people I know well, I can speak casually and freely.

There's no English concept of an 'easy mood'. I'm guessing the meaning, perhaps you mean 'speak freely'?

Thus, I shouldwant to consider meeting new people a pleasant experience. Thus, I want to consider meeting new people a pleasant experience.

'should' sounds odd to me here. Should is used when you have an obligation, but it doesn't really make sense to say you have to enjoy meeting new people. You might say 'you should do your homework'.