Two questions about playing in central/south America

[Pomeranian]

I'm playing as the Inca Empire and it's taking me ages to colonise provinces atm. My dip tech level is only 4, which doesn't help, but I have completed the Expansion and Exploration idea groups. It's currently a long slog to colonise the provinces and I find myself just sitting around for hours just to colonise 6 provinces. My two questions are: Is there any way to speed up colonisation? Is there any way to discover islands which are just off your coast? (Castille have an island very, very close to Venezuala but it is still terra incognita. If I could discover it, I could reform my religion and improve my dip tech)

 

[Robert de Bruce]

If you have the money to afford going about your colonisation cap, you can colonise more provinces simultaneously (just send your colonist back and keep the colony). To speed up single province colonisation, you can activate the settler growth native policy (attitude towards native) and place military in your colonies to deal with native uprisings. When you have expansion and exploration filled you can activate a policy increasing setller growth.
Theoretically you could use trading in cotton to increase settler chance, but this should not be doable as early Inca, since most cotton provinces are in India.
For exploration, I don't really have an idea. Maybe you can trade/steal maps with/from someone, but you need diplo 6 for that.