Relics are in D&D terms just artifacts that happen to be associated with powerful persons of the past and to have acquired their power through use rather than necessarily acts of creation.
Most of your questions have to do with story and world building. If you want interesting relics you have to have interesting NPCs inhabiting the past of your world that did interesting things and became either famous or infamous. These persons achieved some demigod like level of power and as a result, their mortal remains or their cherished items are imbued with, blessed with, or cursed with magical power. So the answer to most of your questions are simply, "Create a story about your world."
As such, I don't think that we really need any sort of mechanics about what becomes a relic and how relics are generated unless you are actually running a campaign where the players go well above the normal maximum level of your campaign world and are transitioning to being demigods. I don't know that D&D is really well suited for that, and it's not a game every campaign will ever need, and if it goes that way then figuring out how many relics a player is eligible to have spontaneously created and so forth will be the least of your rules problems.
Technically, the main thing in D&D That defines something as a relic or artifact is that it if something is deemed an artifact or relic it is no longer eligible to be destroyed by ordinary means. Think the 'One Ring' in LotR that can only be destroyed if it is thrown into the fires where it was made. There are a lot of other things that conventionally artifacts and relics can do, like for example they can often bypass certain divine resistances and immunities and many of them are scry proof and cannot be detected by divination magic in the normal manner and very often they have both positive and negative qualities when in mortal hands, but the main thing is that they can't be destroyed. Individual relics need not be very powerful, but they should have this quality of being more or less invulnerable to damage.
As for corrupting a relic, that should be at least as hard as destroying one. More usually, any attempt to corrupt a relic is going to result in the thing that is attempting the corruption being corrupted (or purified, as the case may be). Extraordinary means would be required. You put an artifact on a typical alter to corrupt it, and you are probably going to need to rededicate and reconsecrate that alter. These things are typically dangerous even to touch if you aren't aligned with the spirit of the relic.
Thinking about pilgrimages and religious festivals is good deep world building, but seldom are you going to need to work out the details of a pilgrimage because rarely are the player characters going to be the pious individuals undertaking a pilgrimage out of sincere religious conviction. I think it's enough to introduce the idea by having pilgrims show up on the roads and streets of your campaign world, with some sort of ceremonial garment that signifies that they are pilgrims of a particular sort and the variety of people that are providing services to pilgrims as guides (physical or spiritual), guards, and even things like sellers of souvenirs or street food. Pilgrimages are a sort of tourism and I think it's important to realize that the PC's are usually mercenaries and the pilgrims are adventurers in the literal sense of that word as opposed to the sense created by D&D.
