Adding another link on the AS5350 to a different service provider introduces a number of complexities which you will need to consider (especially if you have not connected to another AS before).
Some of the answers are fairly simple, yes you probably do need to get a new IP address from the new provider to make the new link work. There are several alternatives which address your concern about not being a transit network for inter-AS traffic. If you decide to run BGP with the providers there are AS path filters that you can use for this. If you do not run BGP then you might want to consider an access list inbound on the link which would deny any traffic whose destination address is not in your address space. (That access list should also deny any traffic whose source address IS in your address space, deny any traffic with bogon source address, etc)
Some of the questions you will need to consider as you plan how to achieve redundancy is how you control traffic outbound to the providers, and how routers in the Internet will get traffic to you (how will your addresses show up in their route table) will one provider be primary and the other purely a backup or will traffic balance between them (a particularly complicated question if your IP address space comes from your original service provider).
HTH
Rick
HTH
Rick