Must I have an account with every gateway I use as an issuer?
Where can I find the address?

The address you need to trust to hold Bitstamp issued currencies is available from the Bitstamp website, but as you noted, you must be logged in to see the relevant page.

You can also find the address at https://www.bitstamp.net/ripple.txt under the [accounts] key. The ripple.txt file is documented here: https://ripple.com/wiki/Ripple.txt

Do I need an account?

You do not need to have an account with Bitsamp to be able to hold Bitstamp-issued assets. All you need is to trust their address. You can then buy Bitstamp-issued BTC, or USD or EUR or whatever else purely on the Ripple network.

Of course, having a Bitstamp account will allow you to redeem those IOUs through Bitstamp. Without such an account, you can still trade them on the Ripple network for either XRP or other assets, likely issued by another gateway.

You may find this primer to be of help: https://ripple.com/guide-to-ripple-gateways/