It's been open for over a month in England.
No. Only for domestic transfers. Ther International window opens July 1st in England. You can arrange transfers (Internationally), but they won't be official until then.
So yes then.
No. Your statement was regarding the transfer window being open, which it's not.
http://www.premierleague.com/en-gb/fans/faqs/when-does-transfer-window-open-close.html