The band used these symbols on the fourth album, in 1971. Here is what was happening in 1971.
Jimmy Page is on record saying that he had felt dissatisfaction, and furthermore received complaints and criticism, regarding the liner notes and written information printed onto the packaging of the band's three previous albums. He decided to respond to this by putting out a fourth Led Zeppelin album that would be as entirely devoid of any written explanations as he could devise. It would have no title whatsoever, have no words printed anywhere on the external packaging, and as few words as he could possibly get away with on the paper album sleeve. He even went so far as to refrain from naming the band members themselves.
Central to this strategy was the four symbols: He asked each member of the band to chose a simple hieroglyphic-like symbol to stand in for that band member's name.
The whole undertaking was an artistic statement, or the lack of a statement, if you like.
In the ensuing 45 years, various explanations have come to light, some reluctantly provided by the band members themselves in various interviews.
To address your points and questions:
Each member of the band chose a symbol to represent himself.
It is well-documented that Jimmy Page was a serious lifelong student of the works of spiritualist/occultist Aleister Crowley. Page would of course have also studied earlier occultists who influenced Crowley. If this is what you mean by "religious sources", it is true. It is likely that this influenced Page's choice of a symbol for himself. I have not read that any other member of Led Zeppelin studied Aleister Crowley, so it's not likely that the other three members of the band chose their symbols based on that influence.
It is fair to say that the members of Led Zeppelin wanted a bit of mystery around these symbols, which is probably why they did not explain them at the time. They chose to use these symbols on the paper sleeve that holds the vinyl album only. Their use of these obscure symbols, and the lack of written words where they would be expected, seems to state that they want the music to speak for itself without comment.
In order to sell this record album in stores, there had to be some way of labeling it or cataloging it, so Atlantic Records affixed stickers to the exterior of the plastic shrink-wrap sealing the cardboard album package, providing a track listing, the record label logo and the stock number. Once the customer purchased the album, they would have to cut open the plastic shrink-wrap in order to unseal the album and open its gatefold to see the artwork on the inside. Most customers would discard the shrink-wrap, meaning that they would lose the stickers and be left with an album package that said absolutely nothing on the exterior or the interior. The only printed information was on the paper album sleeve; minimal notes with track listing and the names of recording studios on one side, and the lyrics to "Stairway to Heaven" on the other side. The names of the members of Led Zeppelin, as band members, are not mentioned anywhere; guest singer Sandy Denny is named (and given her own fifth symbol). The production credit is "Produced by Jimmy Page; Executive Producer, Peter Grant". The artist who did the interior gatefold illustration, Barrington Colby, is named. These names were probably stated according to the expectations and dictates of copyright law; they are the only personal names of people given.
Finally, on the back side of the paper album sleeve, there are the lyrics to the song "Stairway to Heaven". Notably lacking is the customary printed copyright notice for the lyrics; the name of the person or persons who wrote the lyrics is absent also. (Although you can be sure that the publishing company asserted that copyright and defended it, and still does)
