Upgrading shifters 105 to Ultegra?

[AppleJack]

Currently going through a DIY upgrade of my road bike. Already made the mistake of trying to turn a 9 speed into a 10 speed but am too stubborn to go back and it's kind of fun to learn how it all works. I now have an Ultegra 6700 10 speed cassette and need to pair it with a new 10 speed shifter. I have been reading about actuation ratios and want to make sure the shifter is compatible. Would a Shimano 105 5700 STI lever fit with this 6700 series Ultegra cassette? Also would I need to upgrade my rear derailleur which is a 105 9 speed or could it do in a pinch?

Thanks