No to both queries.
You can install a remote desktop app from the Playstore on the Galaxy Note such as Microsoft Remote Desktop or Splashtop2 Remote Desktop to access SW on your laptop provided its running Windows XP/7/8 Pro. I believe the latter app works better with 3d but I have never tried these apps myself.
I have no idea how well it would work with Solidworks but I suspect it would be a little impractical with such a small screen.
Try it and let us know.
If you want to run SW natively on a tablet then it needs to be one running Windows 8 as its operating system, such as the Microsoft Surface Pro 2 or Asus VivoTab - the two you listed run iOS and Android respectively.
The couple of remote desktop apps I've used work okay, but I wouldn't want to be doing any serious amount of SW on them (though I haven't tried it on hardware as recent as the Galaxy Note 10.1 2014).