Hi Banjo, D_Know_WD may be right to a degree, but it is important to understand a few things, Alot of applications when they are installed on a PC, alter the registry files for the O, so they cannot be simply be transferred from one machine to another. Once you install (lets say photoshop) on the PC, one of many things done during installation is that it alters the windows registry files, as it does so, services are added and are automatically run. Because those services and registry files are registered to a specific OS installation, the chances are they cannot be run from another instance of an OS (i.e. If you have 2 OS's and 1 of them has the registry files updated to use photoshop, the other one won't unless you re-install it)
if i was to TL;DR this, I would say that no, you won't be able to use the applications unless they are installed on the new OS. As for formatting the drive, I don't believe you would have to, your PC's BIOS will boot from whatever hard drive it is told to. So if you tell it to boot from SSD, then it will do so. The files on the other HDD should be accessible (In my current machine, i have 1 SSHD and 2 HDD's the OS is on the SSHD, on one of the HDD's (which is dodgy and once was my main drive), i still have the old OS on that as well as some of the documents/music and even apps, but the apps cannot be run).
But by all means, connect your old drive, insure that you are booting from the correct drive. You should be able to access data from the old drive and maybe even the applications (but i doubt it).