If you have installed Outlook connector then you are not using outlook.com via webmail but are using Outlook 2007 for it. Webmail is through your browser. You should not be having any problems sending via the browser. You can also log into BT using the browser and send.
But coming back to your original problem I'm not sure why you set up a MAPI account or how you did it and the problem may well lie there. Suggest that you delete the hotmail/outlook account in Outlook and start again. You can back up the received emails first. The Outlook.com account should be an Exchange Activesync type.