How much transfer time do I need at Karlsruhe Hauptbahnhof?

I am trying to book some train tickets on the Deutsche Bahn website. One of the tickets it is recommending involves a 7-minute transfer from one train to another at Karlsruhe Hauptbahnhof. The arriving train comes in on Platform 1 and the departing train leaves 7 minutes later from Platform 14. Those sound potentially quite far apart - is it reasonable to do that in 7 minutes? Travellers will be: one adult and one teenager, with no mobility issues, with one suitcase and two rucksacks between us. We've never visited Karlsruhe before so are not at all familiar with the station layout, but speak enough German between us to be able to read signs etc.

Also, if we buy "Sparpreise" tickets which are for the specific train only, and we miss the connection, presumably we have to buy another ticket? The DB website implies (at https://www.bahn.com/en/view/booking-information/passenger-rights/passenger-rights-in-rail-transport.shtml ) that you are only entitled to a refund of your original ticket if the train arrives more than 60 minutes late at your final destination, and isn't really clear about what happens if you miss a connection due to the first train running just a few minutes late but have a "specific train" ticket.