Hi Alex,
Welcome to the forum.
I haven't tried MikroE's compilers but I have used a couple of their development boards and have found them to be of very high quallity, especially concidering the price. I currently have a EasyPIC7 which I upgraded to from am EasyPIC4 but I haven't used it much yet. I also have a PICPLC16 which I've used extensively and a couple of other small boards. Anyway...
Can I use Easy Pic v.7 development board (programmer, hardware, incd debugger) with pic basic pro ?
You can definitely use the board and the onboard programmer with its software to program the .hex files produced by PBP into the PIC you place on the board. It'll be a two step process though, first you compile the program, then you load the .hex file into the programmer software and program the PIC. Unfortunatley they don't provide a command line interface for their programmer so it can be "run" from within MicrocodeStudio (which is the "standard" IDE for PBP). The debugger however is tightly integrated into their IDE and their IDE is tightly coupled to their compilers so you can't use PBP with it. So, the board and the programmer will work just fine with PBP, the debugger will not.

As I can guess from sample code provided with trial of picbasic pro, the syntax is quite limited, compared to basic stamp, and for each MCU used, you have to know and remember names of all registers, output-input ports, mode of ports and so on. So, for example when with basic stamp you say simply type text like PORT(X)=1 and it will set port #1 high, regardless of MCU used, here you can't do the same, you have first to know which MCU uses which naming for ports, and then use the command?
That's because there's only a couple of BASICStamps while there are hundreds of PICs and PBP support all of them (all 8-bit ones that is). There is a file which you can include in your PBP source file that gives you the same names as the ones used in the BS2 for example. That may be convenient at first but really only limits you once you start getting into it. It's not that hard really, and naming conventions across chips and even families of chips are all the same. Ports are named PortA, PortB, PortC etc (except for some smaller PICs where they are called GPIO) and the Microchip datasheets are great. So, as long as the PIC has a PortB, you'll do PortB.0 = 1 to set bit 0 of of PortB high, regardless of the PIC just as with the BasicStamp.

Also, in basic stamp, you knew which stamp was able doing which command. Here, you have no data, right? for example, I'm pretty sure, 16F628 and 18F455 are totally different and 455 can do much more than 628 do, right?
In generall all PICs can do all commands. There are of course exceptions and they are the commands which uses hardware peripherals of the PIC. For example the USB commands obviously won't work on a PIC that doesn't have a USB peripheral, the HSEROUT command won't work on a PIC which doesn't have a USART, the ADCIN command won't work on a PIC that doesn't have an ADC and so on. Compiling a list of that would be an absolute monumental task and new PICs gets added to the Microchip line up "all the time".

I hope that clears some of your questions up.

/Henrik.