In order- there's been a CLINIC on wood painting techniques here on this very forum in the last year. Take a look at threads about the Black Swan, Cog, Carrack, Nina/Pinta and others.
Premolded rigging is worse than no rigging.
There are no "aftermarket" parts for this kit. But there are plenty of sources for rigging and such supplies, all of which you will see in the above.
Ditch the sails. Making new ones for an "under sail" condition is really hard. No sails would be fine.Furled sails can be a plan, but it would take some thought. many ships of this era lowered the yards and sails rather than the more contemporary practice of sending sailors aloft to stow them.
But it's been a great year for 15th-16th-17th century builds around here.
That's a great kit, I love the figures.