Become Toing a Writer

"Become to Writer" is grammatically incorrect. The correct expression is "Becoming a Writer," which indicates the process or aspiration of becoming a writer. The infinitive form "to become" doesn't fit here, and "Becoming" is a better choice to reflect the ongoing or desired process.

I'm not sure if what I'm about to tell you next can be called mya dream or not.

"Dream" is an uncountable noun in this context, so you don’t need "my" here. It sounds more natural as "a dream" instead of "my dream."

I like reading books, and sometimes I want to become a writer.

"Become a writer" is understandable, but the more natural expression is "be a writer." "Become" is often used in the context of gradual transformation, and "be" is the better fit when stating a career goal.

NowCurrently, I am an engineer and a project manager.

"Now" is okay but "currently" sounds more natural when talking about your present occupation. It indicates your current status and is often used in formal writing.

When I worked on a Pproject, I wrote out some possibilities and imagined what would happen, and how I would resolve it. (oOf course, in working, that is anvolves planning skills or estimating a problemproblem-solving skills.).

"Project" doesn't need to be capitalized unless it’s a title or a specific name. "Wrote some possibilities" is fine, but "wrote out" is more natural. Also, "in working" should be changed to "in work," and the phrase "planning skill or estimating a problem skill" should be improved to "planning skills or problem-solving skills" for clarity and natural flow.

I like to seobserve everything that occurhappens around me and note it in my blog.

"See everything that occurs" sounds a bit awkward. "Observe" is a better verb choice when talking about paying attention to things around you. "Happens" is a more natural verb than "occurs" in this context.

By the way, writing stories makes me feel like I am living in another world, with strange things happening that the real world never does.

"Feel like" is the correct structure when talking about emotions or sensations, so "feel like I am" is more natural than "feel I am."

To Become Toa Writer

Alternatively: "Becoming a Writer".

When I worked on a Pproject, I wroteite out some possibilities and imagined what would happen, and how I would resolve ithem. (oOf course, in this line of working, that is a's called planning skills or estimating a problemproblem estimation skills.).

(1) "worked", "wrote", "imagined" should all be in the present tense, since this is presumably still what you do regularly, given you're still a project manager.
(2) It should be "them" instead of "it", since "possibilities" is plural.
(3) What you wrote in the parentheses is a whole sentence by itself, and should be written as such. (Yes, you can put parentheses around whole sentences!)

I like to see everything that occurs around me and note it in my blog.

"see" is okay, but consider "observe".

By the way, writing stories makes me feel like I am living in another world, with strange things happening that the real world never dosees.

Here, "strange things...that the real world never sees" refers to strange things that never occur in the real world (and hence nobody ever "sees").

Become Toing a Writer

Whilen I worked on a Pproject, I wrote some possibilities and imagined what would happen, and how I would resolve it (of course, in working, that is a planning skill or estimating a problem skill).

By the way, writing stories makes me feel like I am living in another world, with strange things happening that the real world never does.