Is there only one ferry from Hvar to Korcula per day?

Yes, this one : https://www.croatiaferries.com/hvar-korcula-ferry.htm

Another one is to Vela Luka, the afternoon one:
https://www.croatiaferries.com/hvar-velaluka-ferry.htm

There is also morning ferry, twice a week from Stari Grad to Korcula (June to Sept only):
https://www.croatiaferries.com/starigrad-korcula-ferry.htm

All Korcula to Dubrovnik ferry schedules are here:

https://www.croatiaferries.com/korcula-dubrovnik-ferry.htm

No 

Check these >

Getting by Ferry from Split to Dubrovnik :

https://www.dubrovnik-travel.net/getting-by-ferry-from-split-to-dubrovnik/

Getting from Hvar to Dubrovnik:

https://www.dubrovnik-travel.net/getting-from-hvar-to-dubrovnik/