Pagan and pagamos? When should I use each one?
Nosotros pagamos? Ellos pagan?

Is pagan, only for talking about they (not including self).

And is pagamos, when talking about we (including self)?

Also does this rule of ending in mos and n, always follow the same rules?

Question

Pagan and pagamos? When should I use each one?
Nosotros pagamos? Ellos pagan?

Is pagan, only for talking about they (not including self).

And is pagamos, when talking about we (including self)?

Also does this rule of ending in mos and n, always follow the same rules?

Answer

The rule por present simple, with regular verbs, is the following:

1ª conjugación: verbs finished in -ar, like amar (to love)

yo am-o (i love)
tú am-as (you singular)
él am-a (he, she, it)
nosotros am-amos (we)
vosotros am-áis (you plural)
ellos am-an (they)

2ª conjugación: verbs finished in -er, like comer (to eat)

yo com-o
tú com-es
él com-e
nosotros com-emos
vosotros com-éis
ellos com-en

3ª conjugación: verbs finished in -ir, like partir (leave, depart/break, divide)

yo part-o
tú part-es
él part-e
nosotros part-imos
vosotros part-ís
ellos part-en

Answer

Nosotros pagamos = We pay (you are included).
Ellos pagan = They pay (you are not included).

Answer

Yes, because you're talking about 2 different people in plural, "pagamos" which is "Nosotros" you are included. "pagan" which is "ellos" you are not included.

Answer

Sí es así, siempre sigue esa misma regla, nunca cambia sea la forma verbal que sea.