Or anything like it. Will I lose its perk or no?

Nope. you can check your perks you aquired in the farthest tab to the left in the pip boy menu.

no you gain the perk instantly on reading

doesnt matter what you do with the mag later nor do you even need to "take" it just read it

Once you'd read a magazine, the perk is yours to keep. You can sell the magazine, or store it on a special rack or shelf built using the settlement Workshop feature.

As for Total Hack and RobCo Fun though, you'll want to hold onto the holotapes produced by those.