Pulse garlic, ginger, lime pickle, paprika, cayenne, and one-quarter of onions in a meals processor till easy. Add mayonnaise, season with black pepper, and pulse to mix. Scrape marinade into a big resealable plastic bag.
Pat hen dry; season frivolously with salt (the lime pickle is already fairly salty, so use a lightweight hand). Add to bag with marinade, seal bag, and toss hen to coat. Let sit at room temperature 1 hour or chill as much as 12 hours. (The longer the hen marinates, the extra the lime taste will come via.) Wrap up remaining onion; chill till prepared to make use of.
If chilling hen, let sit at room temperature 1 hour earlier than roasting.
Preheat oven to 450°. Toss potatoes and remaining sliced onions with oil in a big roasting pan. Add ¼ cup water; season with salt and toss once more. Place hen, pores and skin facet up, on prime (be certain that the items have some house between them). Roast till hen thighs are frivolously charred in spots and cooked via, 45–55 minutes. Take away from warmth and let sit 10 minutes.
Toss watercress with lemon juice in a small bowl; season with salt.
Serve roasted hen and potatoes and onions with watercress.