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You can, but with the way the "Anthology" games work out is that they have a save menu (shaped as a PS2 memory card) on the bottom, you can also make the option where you can autosave the game.
And yes, you can go back to the main menu by pausing during gameplay, forgot if it was now either using the touchpad or by pressing options. (You can probably soft reset, if it still works as its a PS2 on PS4 by holding all trigger buttons and press the touchpad and options button at the same time.)
"The Alternate Truth is yet to be Found" - Online Handle: NeoStrayCat