I don't know all the answers, but here are some:
1) This probably won't fully answer your question, but have a look at this application note, it even contains an Excel power estimator: AN86233 - PSoC® 4 and PSoC Analog Coprocessor Low-Power Modes and Power Reduction Techniques
2) Yes, it has a preprogrammed bootloader. I use this kit every day and love it. The bootloader takes about 5 kB from the 32 kB in the chip.
BTW another kit starting at ca $10 feature a KitProg/KitProg2 programmer and it is possible to use it also with other chips.
If you buy both, it might solve any programming / debugging issues with very low budget. (Otherwise the recommended programmer is here: CY8CKIT-002 PSoC® MiniProg3 Program and Debug Kit )
3) If you mean the HD44780 / compatible, it is SW based. Here is a snippet from the initialization:
Also, if you plan starting with this kit, check out these videos, they will give you an idea of how the kit is programmed:
Here is how to create a program from scratch: PSoC Creator 101: CY8CKIT-049 Prototyping Kit New Bootloadable
Also, there is a nice PSoC 101 series (ca 15 videos), starting with this video:
It is targeted at a different kit, but I successfully followed all the examples with the CY8CKIT-049.
I hope this will get you a clear picture of what is the programming like and about the capabilities of this kit.
I got the CY8CKIT-059 and CY8CKIT-049.