Is it question

[onkar]

I often ask myself why chose the life I’m living right now? (Here, at the end of sentence,will ? mark be used)

[bhaisahab]

I often ask myself why chose the life I’m living right now? (Here, at the end of sentence,will ? mark be used)

No, it's not a question, it's a statement.

[Rover_KE]

'I often ask myself why I chose the life I’m living right now.'

[5jj]

'I often ask myself why I chose the life I’m living right now.'

Or: I often ask myself, "Why did I choose the life I'm living right now?"

[onkar]

No, it's not a question, it's a statement.

Is it needed to add here 'I' or change the construction?

[5jj]

Is it needed to add here 'I' or change the construction?

See posts #3 and #4.

[emsr2d2]

Is it needed to add here 'I' or change the construction?

In your original question, you need to add the "I".

I often wonder why I do this.
I often wonder why you do this.
I often wonder why we do this.

Etc.