Keikyu is an abbreviation of Keihin Kyuko. The name hasn't changed.
If you run fast from your plane, you might make it onto the 16.45 N'EX, which will take you all the way to Yokohama. (same goes for 17.43 N'EX)
In that case, you might consider a N'EX + SUICA ticket for 3,500 yen (I think) that would cover your trip to Yokohama and give you 1,500 yen worth of train rides around the area.
http://www.jreast.co.jp/e/suica-nex/
1,500 yen of SUICA rides isn't quite enough for Yokohama to Yokosuka to Yokohama to Haneda Airport. But you can pay the extra amount at a fare adjustment machine on the final ride. And then take the SUICA to the ticket window and claim back thhe 500 yen deposit...
Your Japanese seems to be working fine. People in the 21st century will still understand you.