Ps4 free monthly games

You don't need to physically download the games to your device, but you do need to go into the storefront (either through an appropriate console or through the web interface) and "purchase" the items by adding them to your cart and going through the checkout process. Once you complete checkout, those items will be added to your Download List permanently and can be re-downloaded as many times as you want, even if those items are no longer free for new PS Plus subscribers. You will lose the ability to download or play those games if your PS Plus subscription lapses, but if you subsequently re-subscribe, you will once again be able to download and play those items.

This does mean that free games can potentially be "missable" if you have not added those items to your account before they go back to paid status. While some Instant Game Collection games have remained free for long periods of time, that is often not the case, and you will need to be sure to "purchase" those items during the limited window in which they're available for free.

It really depends on the game, I'm afraid.

Some Vita games store their saves on the cartridge, rather than the console, and some of the download versions of games on PS+ aren't the exact same version as those sold at retail, so the saves aren't always compatible/accessible.

That said, unless your downloads are capped, then you've nothing to loose by trying.