Refineries benefit each resource rock in the gravity well it's build as well as each resource rock in adjacent gravity wells.  So if you have three planets connected like so:

A=B=C

And you build a refinery at planet A and planet C, then this is how it works.  A and C each get the effect of one refinery, while planet B gets the effect of two (even though you didn't build any refineries there, it's adjacent to both A and B ).  Refineries only stack up to three times, meaning if you build two refineries at each of planets A and C, then planet B would only receive the benefit of three. 

Trade ports are usually a better investment because they are less expensive than refineries and you don't need to place them where there are a lot of resource rocks nearby for them boost.  Instead, the goal is to produce a long trade chain.  The longer your trade network, the more money each trade port will produce.

Both of these structures are quite expensive and you should be reserved about buying them until later on because of this.

Vasari matter processors work the same as TEC orbital refineries.  They're just named differently.  We call them both "refineries" just out of simplicity.

Just watch out, the Advent don't have a dedicated refinery, and the "Resource Focus" upgrade is a rubbish excuse, it just boosts in grav-well mining.  You're better off leaving them as trade ports.

A note on the forum jargon though;when a unit  or structure type class is common across all races (which is most units and structures)  we often refer to all of the class generally using its TEC name, unless the unit is particularly distinct.  Examples include refering to Colbalt Light Frigates, Skirmishers and Disciples as light frigates, or Javelis Long Range Missle (LRM) Frigates, Assaliants and Illuminators as LRMs. 

The refineries are another example - Refineries and Matter Processors are both refered to as Refineries - although here the Advent unit is so distinct it isn't considered a proper refinery (and is always called an "Advent Refinery" or something similar).

We usually only refer to units by their race specific name when we want to distinguish them, usually for balance purposes or race specific strategies, as they still have their differences between race.

Hope that helps

Since Resource Focus is a % increase based on current extraction, the benefit will depend on the planet's alleigance, any extraction bonuses the planet provides, and the number of extractors in the gravity well.

Those ideal circumstances probably involve some combination of Allure of the Unity, close proximity to home planet, 4 extractors, and/or starbase with upgrades in Induced Reverence.