Mix the paprikas, chilli flakes, mustard, vinegar and lemon and lime juices in a bowl to a smooth paste.
Transfer the marinade to a large plastic food bag, add 4 tablespoons of the olive oil and the chicken, then seal the bag and shake it carefully to cover the chicken in the marinade. Set aside to marinate for as long as possible.
Prick the potatoes with a fork, then rub them in some of the remaining oil and season with salt and pepper. Wrap each one in aluminium foil.
Place one garlic bulb onto another sheet of foil and drizzle with more of the remaining oil. Wrap the bulb tightly in the foil.
Light the barbecue. Allow the flames to flare up and die down, then wait until the coals are glowing and starting to turn white.
Cut the second garlic bulb in half horizontally and stuff the two halves inside the chicken. Manoeuvre the half-full beer can to fit just inside the chicken, so that the bottom half of the can is sticking out of the chicken.
Nestle the wrapped potatoes and garlic bulb into the coals, then stand the chicken upright on its beer can in the centre of the barbecue. Wrap a piece of aluminium foil around the base of the chicken to form a protective collar, then cover the barbecue with the lid and cook for 15 minutes.
Remove the garlic bulb and set aside to cool. Continue to cook the chicken and potatoes for a further 30 minutes, or until the chicken is completely cooked through and the potatoes are tender.
Unwrap the garlic and squeeze the roasted garlic from the cloves into a bowl. Stir in the chives and butter.
For the salad, mix the lettuce leaves, tomatoes and cucumber together in a large serving bowl then drizzle with the olive oil.
To serve, transfer the cooked chicken, still standing upright on its beer can, to a large serving platter. Unwrap the potatoes, cut a cross in the top of each, squeeze gently and spoon over the garlic butter. Arrange the potatoes around the chicken, garnish the plate with the lemon and lime wedges, then serve with the salad.