I've been in the hunt for a no annual fee Mastercard/Visa to complement my no annual fee Amex card. So far, all I have found is this - the coles mastercard that comes with a $50 sign up bonus.
http://www.ozbargain.com.au/node/106449
Is anyone aware of any others that are no annual fee? I don't think I spend enough to warrant paying any of the annual fees (since I won't earn remotely enough in rewards).
Also what is wrong with applying for more than 1 credit card within a 12 month period? Someone posted a comment about this in one of the posts I've read.
To answer the last part of your question,
Every Credit Card application will show up on your Credit Rating Report. (I'm unaware of recent changes) but if you apply for say 4 credit cards, you will have 4 enquiries.
Financial institution wouldn't look favourably on so many enquiries.