I installed Ubuntu Core and found that it used Snap for application installation. I want to install many applications on this system such as firefox, chrome, and many more. How can I do it? And is it possible to install apt-get or yum any how?
No, Ubuntu Core is completely snap-based: apt is not available. Ubuntu Core mostly targets headless or kiosk-type devices, and as such doesn't ship with a window manager etc. Kiosk software typically uses Mir. You probably don't want it for a normal desktop environment; you can install snaps on the classic desktop release.