Q1. Proper nouns typically are not preceded by 'the'. Some, however, are - either optionally or obligatorily. Some writers prefer to distinguish between the sun (i.e. central star) of any planetary system and that of our own by writing the latter with a capital. Thus, we might have
 Every star in the sky is a potential sun.
 All life on Earth depends on the Sun.
This is, however, not a rule, but a tendency, generally restricted to contexts where the sun is being considered from a scientific point of view. In
 The sun was shining that day.
it would be unusual to use a capital, even though we are referring to the same celestial object!
Much the same thing applies to 'moon', so that we have 'a moon' (common noun, any celestial body orbiting a planet), 'the Moon' (our moon, in a scientific sense) and 'the moon' in more everyday contexts.
'Earth' is a little different since, as mentioned, it may stand as a typical proper noun (i.e. without any article), but the acceptability/naturalness of this tends to depend on the construction, so that after prepositions we normally have no article (e.g. come back to Earth), whereas, as grammatical subject or verbal object, it tends to be preceded by 'the' (and spelled with a capital letter) as in
 People used to believe that the Earth was flat.
 It would destroy the Earth.
Note that, as a common noun, 'earth' can function in two ways: (1) as a countable noun, meaning 'home planet', as in
 Could these aliens have travelled from their earth to ours?
(2) as a noncount noun, meaning 'soil', as in
 The body was buried in deep earth.
Note also that, since non-scientific references to the planet on which we live, as opposed to objects visible in the sky, tend to be rarer, we will normally find 'the Earth' with a capital rather than a small 'e'.
Q2. Yes, as common countable nouns, any of them may be pluralized, e.g.
 Jupiter has twelve moons.
 We see the light of a billion suns.
'Earths' is very rare, but, I suppose, theoretically possible.
Q3. Are you asking about forms such as 'the good' and 'the poor'??