All your questions can be answered positively.
On the board (I saw it on the picture) is an ISSP-interface to program the PSoC with a MiniProg1 or MiniProg3 (the latter is more universal) which you can get from your local Cypress-distributor. Better (because cheaper) would be to order a
CY3210 PSoCEval1 development kit wich not only contains the kit with an LCD-module and bredboard area but a MiniProg1 as well.
It may turn out to be a bit difficult to debug PSoC1 applications. In this case you ought to use an ICE-Cube (In-Circuit Emulator) which is not really cheap but VERY versatile.
The design-software is PSoC Developer 5.2 wihich can be downloaded freely from the Cypress website. All programming can be done with the (free as well) C-compiler. And all the informations regarding this special design you've already found.
If you are getting interested in the unique features of the combination of analog and digital modules within the PSoCs I would suggest to spend some time in watching the videos here at Cypress, They'll give you an insight into the principles of operation.
Thanks Bob ll get back to you if any clarification. :) :)
Take your time to study the fascinating world of PSoCs!
You may download PSoC Designer (for PSoC1) or PSoC Creator (for PSoC3 and PSoC5) and some example-projects and start to learn to manage them.
You are always welcome