Can Linux OS (As in Mandrake 10 and later) use Intel Core 2 Duo?
 

Can Linux OS (As in Mandrake 10 and later) use Intel Core 2 Duo (Including the Quad-Core) or AMD Athlon 64X2 (Duo to Quad Core) as well as any ram,HDD and TV-tuner I liked?

I do not see why you would have a problem. I recently used DSL to test the operation of Linux on my XPS 410 with no problems (short of network drivers). The cores were recognized as two processors and all my RAM and HDD were present. If you have issues, I would recommend DLing a live-CD of the Distro you want to use, if one is available. Ubuntu has an install CD that operates as a LiveCD, so it might be a good option for testing your system.

You will probably need to be a bit more selective with your TV Tuner options. This applies to Myth TV, but I would imagine that most of these would be compatible with any Linux with some driver work.

Core 2 Duo or RAM: no problem
HD: can be problematic if you mean SATA discs but the situation is improving fast - avoid using distros that were released more than two months ago unless you can get an updated version
TV-Tuner: that depends on the manufacturer - some have excellent support, some won't work at all

I want to re-but something jay73 said. The HDD issue is "minimal". If you are using SATA discs, I can currently vouch for: Debian Sarge, Ubuntu 6.10, Red Hat (and subsequently FC), and SuSE (and subsequently openSuse) for distros upwards of 2+ years old. Where you might run into problems with SATA is not the drive but the SATA controller/RAID controller drivers, check your manufacturer for support there.

I admit, I didn't express myself properly. It is the IDE controller that is causing trouble with SATA discs but, well, the end result is still: no HD and usually no optical drive(s) either. On the other hand, I'd like to point out that not all motherboards have one of those lousy IDE controllers (but certainly the large majority of those that were released last year do). My experiences with proper SATA support (ASUS P5B) : Suse 10.2 - no; very latest Etch - yes; Mandriva 2007 - no; Mandriva 2007.1 - yes; Ubuntu 6.10 -no; FC6 - more or less; PCLinuxOS 2007 - yes: Mepis 6.5 - no; Gentoo - no; Slackware - with some tweaking. A mixed picture all in all.

I'd say that SATA Hard Drives are 99% hassle free and very few issues abound. However SATA DVD drives are still a problem with no clear solution. I have IDE DVD Drives with SATA converters plugged into a 965 motherboard (intel ICH8 controller in AHCI mode using libata) and can't get them to show up in any version of Linux (I have slackware 11 with the 2.6.20.3 kernel installed at the moment, tried Ubuntu feisty as well). You are most likely going to have to boot from the DVD, copy it to the hard drive, install from the hard drive, and compile a 2.6.18 or new kernel. If you can find a distro with a 2.6.20 kernel off the bat that will make life easier for you.