Verenti Sense/Ridley Helium component question..

Hi - first post on a bike forum, probably not my last!

I bought a used Verenti Sense about 18 months ago and have loved it.

All was good, until last week when the crank snapped

Crank was a FSA Gossamer, so I've looked into replacing, but as the crankset and cassette are getting worn, thought I'd replace with Shimano 105 kit.

I'm not up to date with kit, so asked Wiggle for recommendations and they suggested a 105 5780 11-speed chainset, cassette and 11-speed chain.  They also told me the chainset comes with a new BSA/68 BB, which it doesn't..

It's only now it's arrived that I realise:

 1 .  I need to replace the BB, as it's worn

2.  my existing cassette is 10-speed - oops.

I spoke to Wiggle in a chat session and the are not sure if it's compatible with the derailleur and they just recommend the 5750 chainset, which is £30 more than the 10-speed version.

My questions are; should I just go for the 5750/10-speed and which BB?

If I switched to 11-speed gearset, would I need a new derailleur?

TIA - Simon