What advantages or differences do lucky Pokémon have?

With the latest update, Niantic added a brand new kind of quality for Pokémon.

Will they appear in the wild as shiny Pokémon do?
Can all Pokémon right now be lucky?
Are there any differences apart from the background effect?
Will there be a noticeable difference when on the map?
Will a lucky Pokémon be for everyone or randomly for each user (like shiny)?

To answer your questions, based on the patch notes and the official blog:

Will they appear on the wild as shiny pokemons do?

No, only pokemon that are traded can get the lucky trait.

Can all pokemon right now be lucky?

As it looks right now, any pokémon that can be traded can get the lucky trait.

Are there any differences apart from the background effect?

Lucky pokémon require 50 % less stardust to power up than pokémon without the lucky trait.

Will there be a noticeable difference when on the map?

Not applicable since lucky pokémon don't appear in the wild.

Will a lucky pokemon be for everyone or randomly for each user (like shiny)?

Lucky pokémon are a random chance when trading, with a higher chance for pokémon which have been in storage for a while. When a trade triggers the Lucky trait, both pokémon receive the trait.

Source: https://www.polygon.com/pokemon-go/2018/7/23/17602604/pokemon-go-update-lucky-pokemon and the links within.