How to install Windows on MAC? (Can't see the check box "Install or remove Windows 7 or later version" on Boot Camp Assistant)

Sounds like you have a 32 bit copy of Win 7. Assuming your Mac is new, or very recent, and came with Mountain Lion, it has a 64 bit EFI. Because of that, you also must have a 64 bit copy of Win 7. A 32 bit version will not install.

Hmm, I'm not sure then. An EFI firmware update will install only if it's for the model intended for.

You also have the correct version of Win 7. Is it an upgrade disk, or full retail version?

Apple has their own support page for installing Win 7, you can give that a read.

Before going any further, I would make sure to have a full, restorable backup of your OS X partition. After that, I would use the Boot Camp Assistant to remove the current Windows partition and start over.

I have this text from some of my older posts.

1. Use Boot Camp to create a partition for Windows to be installed on. It can be part of the drive OS X is on, part of another drive, or you can devote an entire separate drive to Windows. You are asked this at the beginning of the process. If you use part of a drive formatted as HFS+, it will automatically set up an initial split of 32 GB. There's a couple of problems with that. One, that's not big enough to hold even just Windows 7. Two, Boot Camp can only setup a FAT32 partition for Windows since Microsoft has never licensed NTFS to anyone. So what you do is have the Boot Camp utility in OS X create the initial partition. If you've applied the partition for Windows on a drive already in use by OS X, drag the line it will show you between the new 32 GB FAT32 partition and the OS X partition to make it smaller or larger. You'll have to make it larger of course, so make sure to give yourself enough space for Win 7, and the apps you think you'll be installing. You'll need at least a 50 GB partition for Win 7 64 bit.

2. Once you've set up your partition, or a whole drive, the Mac then boots to the Windows 7 DVD. As soon as you are able to make the choice from the Windows setup sequence, choose the option to format a disk. Any Apple HFS+ partitions will appear as unknown, while the FAT32 drive will be recognized, and will be named BOOTCAMP. Choose that partition and do a quick format to NFTS. Then proceed with installing Win 7 on that drive.

3. After Windows 7 has finished installing (through a few restarts) you won't quite be done. You'll notice that the graphics in Windows likely won't be very good, and in general running kind of slow. That's because the Windows DVD has no drivers for Mac hardware. Remain at the Windows 7 desktop.

4. From the Windows 7 desktop, put the Snow Leopard disk in the drive. Windows will pop up the usual message about what you want to do with an external drive. Choose "Run Setup". It will run for a while as the drivers for your Mac hardware are installed for Win 7.

I don't know how this part works for a Mac that came with Mountain Lion. Read the Boot Camp instructions for Mountain Lion. It should walk you through what you need to do to get the initial drivers for your Mac installed.

5. Once that's done, you'll have a menu icon in Windows for Apple Software Update. Run that to see if it needs to download and install any other Boot Camp updates, which would be any updated Win 7 drivers for your Mac. These will be Windows .exe files. So don't try to install the driver updates from OS X.

- you are only allowed to have one partition on the hdd,I had two

Not sure what you mean there. You're only allowed one Boot Camp partition? If that's what you meant, then yes, that is true. Boot Camp Assistant will not create more than one partition for Windows on a physical drive. There are ways around that, but it's somewhat tedious.

From this point on I could not boot in any of my systems Windows or MAC not even in the recovery mode ...

That would mean the Recovery partition got destroyed somehow. The way around that is to restart and hold down Command+Option+R to enter Internet Recovery mode. That would install the entire OS from Apple's server for your model Mac.

I resolved this problem too using the TestDisk application

So that disk did what it needed to in order for your drive to be bootable again. Bad news though, as noted further down.

I'm wondering how can I make my recovery partition "hidden" because now I can erase it maybe by mistake and don't want to loose it.

That comes back to either Recovery, or Internet Recovery mode. Either will recreate the Recovery partition. But you want to hide the one you have. All you should have to do is drag it to the Trash to dismount the drive. It shouldn't reappear on the next startup or restart. At least, it's not supposed to.

Also another problem is that Recovery partition is fixed: I cannot resize the Macintosh partition only on making it smaller (before I could do it both ways).

What is partition "test"? Your Win 7 install, or another Mac formatted partition? Assuming Win 7 is the bottom partition, it will always remain there and you can't resize it. It would now be NTFS and the Mac has no way of changing its size since that requires being able to do a write to update the partition size, and OS X can only read NTFS by default. That means the Recovery HD partition will also always be stuck where it is.

I do see that all partitioning options are grayed out. That probably has something to do with what Partition Magic did to the drive. It worked, but left the partitions flagged in a way OS X doesn't understand. It's not meant, or designed to work with Mac drives.

I hate to say it, but at this point, I'd back up any personal data to another drive, then boot into Internet Recovery mode. When the user screen comes up, erase and repartition the entire drive as one partition. Then back out of Disk Utility so you can reinstall OS X, which will also properly recreate the hidden Recovery partition.