I’d avoid it personally, as mentioned, claiming to be a relation to a lore character is not generally regarded well. Now you -could- be of a family that has a long standing connection to the Farstriders, like the Windrunners, but the Farstrider order was only really codified 500 years ago (Rangers have obviously been around longer, Alleria fought in the Troll Wars apparently) Ranger-General was always the title of the commander of all Quel’thalas’ military, not necessarily the Farstrider’s, hence we are uncertain of the ages of the Windrunners, save that Alleria must have been at least 2,820 years old (Elves are confirmed to be adult at 20 at the latest (Source, Edge of Night, the Sylvanas short story) and only that young if she only saw service for a year or so. Vereesa we know was too young to serve in the Farstriders in the Second War, making her pretty young, like, within a human lifespan, probably about 40, but we have no idea of Sylvanas’ age at the point of her death (Edge of Night does not state that, just that she was adult aged 20, given that she is the middle sister, we just know she is younger than Alleria, but older than Vereesa)
I’d make up your own family, and just have them be long standing Rangers as a family, not linking them to the Windrunners.
They absolutely can. They do not have Paladin as a class, but that is because they were largely walled off from the Alliance after the Second War, so may never en masse have learned those methods. Individuals maybe, but it being an established thing, no. Faith in The Light however, predated Paladins. Their culture does seem to include other elements such as Harvest Witches, but yes, Gilneans can use the Holy Light. No reason Worgen can’t unless the individual feels that the Curse prevents them. (It doesn’t, but belief is always a personal thing.)
Probably Arcane, to be honest. Yes there is an example of an Elf getting purple eyes from a Naga Trident, but Purple is different to Violet (Subtle difference, I know) but Blue and Purple seem to be interchangeable when it comes to eye colour, Equally it could be Purple in relation to the Void. We don’t know the exact lore to be honest, as that eye colour has never really been explained.
We do know that without the glowy eye effect, Blood and High Elves have a natural colour to their irises, I think the only ones we know are Lor’themar, Brown, and Liadrin, Hazel, and Alleria, Green.
Hope that helps!