From my researches on the web it looks like Seagate FreeAgent DockStar is the cheapest option but it only have 128MB ram and no JTAG and no SD card reader.
Actually, the JTAG pinouts have recently been obtained for DockStar. So we'll have JTAG "real soon". JTAG isn't really necessary though, because you can chainload a second u-Boot from mtd3, which is almost entirely safe.
What are other limitation of Seagate device in comparation with Sheeva ?
You'll need to purchase a TTL serial adapter and open the case if you want access to the serial console. Also, you'll need to patch your kernel to control the status light on the front (an unpatched kernel still works without light control). Other than that (and no SD slot)... none that I can think of. In fact the DockStar has a lot more USB ports than Sheeva, which is a plus. As is the external power supply (which means less heat).
Can I install same operating system (ubuntu 9.04) on Seagate device as on Sheeva ?
Can I run XWindows on Seagate and login using vnc ?
Can I share data stored on USB drive pluged into Seagate device in the same way as I could do on Sheeva (for example as samba share) ?
Yes, yes, and yes.
Which application I CAN'T run because of only 128MB of RAM on Seagate ?
If you use a hard disk drive, you can use a swapfile which definitely expands your options. Firefox, for example, is a bit of a memory hog and isn't too happy running in 128MB without some swap. Other than that it's hard to say, as there are thousands of applications out there.
What are your experience with Seagate regarding stability, heat problems, power consumption or any others ?
No heat problems on my DockStar, but I have the cover off so I can use the serial port. Even so, the 'Star has a large metal shield over the whole top which is thermally coupled to the CPU, and has lots of side venting, so it's probably better at dissipating heat than the Sheeva. No stability problems either. It shouldn't draw any more power than Sheeva, maybe even a little less (no SD, no serial->USB, less RAM).