If I have two boxes both with Windows OS, that's no problem for me.
However, suppose I have different OS platforms: I currently use TortoiseSVN on my Windows 7 box, but I'll switch to using Ubuntu now. I want my existing TortoiseSVN log to work on my Ubuntu box. Is it possible for me to transfer the log from TortoiseSVN (on Windows) to TortoiseHG (on Linux)?
To recap:
* Or is there Tortoise + Git available?
Yes, this is perfectly possible. Handle the two transfers seperately though:
As for your second question, I don't think TortoiseGit is available for Linux. There are other Git GUI clients for Linux though.