Is NTFS on Ubuntu stable?

Is NTFS support stable enough to use safely?

I believe you have to install an additional package to make it work.

Answer

It's because almost every distribution uses the NTFS-3G driver:

The NTFS-3G driver is used by over 240 distributions. Many, like Fedora, Mandriva, openSUSE and Ubuntu with over 8 million users, use NTFS-3G as the default NTFS driver.

=> NTFS driver for Linux

And yes, it's stable :-)

Do you know why I can't see an option to format partitions like that while installing?

Do you mean the access to your Windows partition from an already installed Linux OS, or do you want a fresh Linux installation? There should be an option to erase/format your old (NTFS-)Partition/s while installing a fresh Ubuntu/Fedora/...