Can I make the autoresponders and broadcast emails look like they come from my email address and not 1shoppingcart?

Yes, both the autoresponder and broadcast features offer the ability to customize the FROM Name & Email info. It's called From Name and From Email.

Hint: The "from email" is the email address the client will reply to if they reply to your autoresponder email. It's extremely important to set this to a valid email address for your business otherwise if people hit reply to one of your emails, YOU WILL NOT RECEIVE THE REPLY. PLEASE MAKE SURE TO SET THIS FOR EACH AUTORESPONDER YOU'RE ACTIVELY USING JUST IN CASE THE PERSON RECEIVING YOUR EMAIL HITS THE REPLY BUTTON.

On the broadcast page, it looks like this:

On the edit autoresponder pages (in the general settings), it looks like this for each autoresponder: