The woman in the cafe that you’re recalling was Libby. Her husband had just passed away and once she heard Desmond’s story about Penny, Penny’s father and the boat trip, she said her husband would have wanted Desmond to use the boat.
As for the timeline of Penny. Des was kicked out of the monastery (he was found drinking the wine). As he was leaving, he helped load the boxes of wine into a truck that was driven by Penny. This was the first time he met Penny. Penny invited Des to help her deliver the wine and this is how they started off. I believe then he was in the military, where he ended up being jailed and getting a dishonorable discharge. Once he got out of jail, that is when Penny’s dad said that Penny was getting married and offered him money to leave her alone (also all the letters he had written to Penny while in jail were never given to Penny, the father had them all).
As for the boat race itself, I think that was more to prove to himself that he was worthy of her (and also to show Penny’s father this).
If you have the time, you can watch the episodes on abc.com since ABC has every episode on there. I would suggest that you watch season 1 Live Together, Die Alone. Around the 15:30 mark, Desmond meets Libby and you’ll be able to see the exact conversation regarding the boat. Also, episode Catch-22 on season 2 explains how Desmond met Penny after the monastery (around the 38:40 mark).
The last thing you asked about was the radiation. After last night’s episode, I think this is going to be explained