Is it possible for opposite-gendered Pokemon to show up in a chain

Option 1: The 'Reset Berries' are back in this generation, they are acquirable from Berry piles, or from PokePelago. There is a berry for each stat, and they all lower EV by 10 points.

• HP: Pomeg
• Attack: Kelpsy
• Defense: Qualot
• Special Attack: Hondew
• Special Defense: Grepa
• Speed: Tamato

Option 2: New to S&M, you can get 'Reset Meals' from the Festival Plaza. I'm unsure what Plaza level is required for them to start appearing.

Sadly, there is no known equivalent to the 'Reset bag' from XY/ORAS as of yet.

Most moves are not affected by happiness, but the move Return does more damage based on happiness. It has has a linear formula with 1 base power at no happiness and 102 base power at max happiness. Conversely, Frustration does less as a Pokemon is happier. The base power scale is the reverse of Return.

In order to Move Tutor various moves, such as Draco Meteor in Pokemon Sun and Moon, the Pokemon needs max happiness. This has occurred in previous games. For reference, moves which have required max happiness to tutor in ORAS include Blast Burn, Draco Meteor, Fire Pledge, Frenzy Plant, Grass Pledge, Hydro Cannon and Water Pledge.

Occasionally, there are specific in game items that depend on happiness. An example is the Footprint Ribbon given by Dr. Footprint for max Happiness in Gen IV games. I am currently unaware of any such items in Pokemon Sun and Moon.