Is Firefly/Serenity related to the game series Mass Effect

lets go through one by one

• Shephard - The main character in mass effect is not named after firefly but instead named after Alan Shepard who was an American naval officer and aviator, test pilot, flag officer, one of the original NASA Mercury Seven astronauts, and businessman, who in 1961 became the second person and the first American to travel into space.
  This is well documented across the internet and more can be found on the mass effect wiki.

• Reapers vs Reavers
  Mass effect - The Reapers are a highly-advanced machine race of synthetic-organic starships. The Reapers reside in dark space: the vast, mostly starless space between galaxies. They hibernate there, dormant for fifty thousand years at a time, before returning to the galaxy.
  The idea of a terrifying and incomprehensible alien intelligence waiting in the depths of space is a feature of Lovecraftian horror. This similarity is emphasized by one of the recordings by the survey team aboard the derelict Reaper which spoke of how "even dead gods can dream." This is a clear homage to Cthulhu, as "In his house at R'lyeh dead Cthulhu waits dreaming."

  Firefly - Reavers are a fictional group of humans in the television series Firefly and movie Serenity who live on the fringes of civilized space and have become animalistic.

  I See NO similarity between these two and the name reaper is clearly taken from reaping which is what that race did.

• The lead in both is captain of the ship, good with a gun and has a keen moral compass (in Mass Effect the player can influence morality).

  Simply this is the premise of many stories - you have a leader, who has a skill and they are usually good. I think this would be a real stretch.

• The Alliance In Mass effect they are the complete opposite to in firefly, as in mass effect they are on the side of good. Alliance is just a standard term used to describe many groups with a single goal.

• River & Jack

  This is at least quite close but fundamentally this comes down to the two characters having completely different personalities.

  River- She has been portrayed and described consistently as having always had both a strong thirst for knowledge and a love for and intuitive grasp of dance.

  I think anyone that has played mass effect would agree Jack is the polar opposite not to mention the gifts in question are somewhat different.

Based on this i think it is pretty clear that the stories and characters are not related and this could probably be done with any two franchises if you look hard enough.

You will probably find more relations between mass effect and Star Trek seeing as how the captains are similar and even some of the races have similar characteristics.

Heavy influences. If you can't see them you aren't paying attention to the details of the stories. The movie especially plays out like a Mass Effect movie, even ending like Mass Effect where the captain fights his way through a battle between the Alliance and Reever fleets to send a signal out. Only big difference is Malcom runs from the Alliance where Shepard works for the Alliance. Everything else is about 90% the same story.