No, Skins don't affect combat in Bizarre Lineage, they're entirely cosmetic and don't change hitboxes, cooldowns, or damage output in PvP or PvE.

The difference between a Lucky Arrow and a Stand Skin Essence is that a Lucky Arrow rerolls your Stand and guarantees a random Skin with it, while a Stand Skin Essence only rerolls the Skin on the Stand you already have equipped.

No, you can't trade your Bizarre Lineage Skins to another player, they're locked to the account that unlocks them.

Yes, you keep the Stands, Skins, and items included with my purchase, exactly as shown in the listing.