1- i don't understand how to set value for some additional field that i created through CB field management

That's explained at the bottom of the tutorial.

2-how to set avatar from outside?

You can't unless you implement the entire image processing chain.

3- i'm using something such as RSFORM for get user information and i want set that field on CB...i don't have any problem for get information from that extension but how to set in CB field...are you suggest me to use query?i guess it is maybe not safe

Review the _comprofiler table if you're wanting to direct database updates, but it won't fire any CB triggers doing this.

1-1 can you more describe about this?is there any function to use that for image processing chain?

No, as it would mean writing a custom function to process images. You could checkout how CB Connect does this, but that's our only example for this.

1-2 if i have pic url can i do any work for that to set as avatar in CB?

I guess if you added it to a text field then used HTML in the layout to turn it into an img tag that'd work, but beyond that no the avatar field is not going to process a URL you pass to it into an image.

1-3 what is the final return image processing steps?

It's significantly too complicated for me to explain here, sorry. If the image is a URL you need a server side HTTP request to request the contents then process it using API to resize, rotate (if EXIF data exists), and save. I entirely feel this is not worth the effort for you to try to implement and suggest just leaving the image uploading to profile edit.

2- when i use cb api, all trigger or something such as validation will be run?

The API tutorial is for direct stores. The tutorial does include trigger usage. No it will not validate anything as it's a direct store.