Is there any API to download data (the task) from BOINC and upload data (the result) to BOINC?
And is it possible to run all the tasks by myself offline on the command line after downloading boinc client(not through the BOINCMANAGER application)?
Thanks

You can do all you want with the client which is the main application. The Manager is nothing more than a easy GUI interface to the client. Not necessary at all to crunch for BOINC. You can do anything you want from the command line with just the client.
https://boinc.berkeley.edu/wiki/Boinccmd_tool
Just connect to the scheduler, get work, go offline and crunch the work. Connect to the scheduler to report the finished work when done and get more work. Rinse and repeat.

The closest thing to an actual "API" are the commands you can send to the app (the client) using boniccmd.exe. If you want to roll your own code to interact with the client then the add on tools here might be useful and especially the c# code at GitHub here. I was told it can run under Linux but AFAICT there is no native C# compiler for Linux.

I don't know if it in any way helps, but when you go to projects, and press 'update', in my case, the manager would load additional tasks, that stay queued until more PC resources get available, or until previous tasks finish.

BOINC is the interface between teh various projects' servers and your PC, it manages the up and download of data, and the running of the project supplied applications. BOINC in itself does no calculation.