UPDATED
See post #3 below.
There is a need to upload a file to the web automatically (without browser). Host - Mini File Host v1.2 (if this does
"As result it returns initial upload page, not a result page with links i could parse and present to a user..."
Maybe that's just the behaviour of the upload functionality: that after the upload has finished, you can upload another file? I think you have to call another url for the "browse for file"-page (I suppose that's the one you need).
Edit: Actually, if the server sends a "redirect" (http 3xx), that's something the browser has to handle, so if you're working with your own client application in stead of a browser, you'll have to implement redirection yourself. Here the rfc for more information.