Okay, let's take it from the top.

Easy one first; Do cold iron/silver weapons equivalent (+3) count as magic for purposes of ignoring DR? This is certainly implied, but not categorically stated as I read it.

1) The equivalency table is cumulative. Bypassing DR/Magic requires a magical enhancement bonus of +1 or greater, which a +3 weapon has. A +5 weapon bypasses silver, cold iron, adamantine, and all alignment based DR.

Is the only way to get an alignment based attack in a weapon to cast either align weapon, use a +5 weapon or be a monster with a 10/lawful (for example) reduction and use a natural attack? Or is a alignment monster using it's natural attacks counted as damage of that type , e.g. an Morlock is CE, do it's attacks count as Chaotic?

2) The Universal Monster Rules in the Bestiary 2 clears this up:

Some monsters are vulnerable to good-, evil-, chaotic-, or lawful-aligned weapons, such as from an align weapon spell or the holy magical weapon property. A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that matched the subtype(s) of the creature.

Basically, you need the alignment subtype for your attacks to count as that alignment. In addition, weapons with a permanent alignment based enhancement, like Holy or Unholy, count as aligned.

If you are a monster with alignment based reduction (eg 5/Lawful) do your natural attacks have no effect on any other alignment DR other than lawful? I.e. if a summoners Eidolon has 5/Neutral are a monster with DR 5/Lawful attacks still reduced by 5?

3) DR/Alignment does not automatically make your natural weapons aligned. If I have DR/Lawful (implying that I am Chaotic), my attacks do not automatically bypass DR/Chaotic unless I also have the Chaotic alignment subtype. Also note that Eidolons have to choose between chaotic, evil, good, or lawful for their DR, they cannot choose Neutral. DR/Neutral isn't a thing in Pathfinder, that I am aware of.

If a monster has two types of DR what do it's attacks natural attacks count as, eg a Kyton has DR 5/silver or good, do it's attacks count as silver (+3) or alignment (+5)?

4) Having DR/Silver or Good does not let your natural weapons bypass silver or good DR. The important things to look at are your alignment subtypes, and DR/Magic. Kytons have the Evil and Lawful alignment subtypes, so their weapons bypass DR/Evil and DR/Lawful. If the Kyton had DR/Magic, then it would be able to bypass DR/Magic as well.

Speaking of Eidolons; the evolution "Damage Reduction" (p63 advanced players guide) gives the Eidolon DR5/alignment; does this now mean that the Eiodolons natural attacks will now count as ignoring DR for that alignment (and cold iron, silver, adamantantine, maybe magic) as alignment based attacks are equivalent to +5. Note that Eiodolons also have a cheaper evolution "magic attacks" (p60 APG) as well.

5) In short, no. Eidolons are the same alignment as their summoners, but they do not have a alignment subtype. Getting DR/Alignment does not let you bypass that alignment's DR for free. The Magic Attacks evolution does allow your Eidolon to bypass a certain aligned DR at high enough levels.

If a monster has DR of (Greater Earth Elemental for example) 10/- what do it's attacks count as? A monster with 10/magic has attacks that are counted as magic, if I read it correctly, but I don't see text for monsters with the '-' reduction.

6) A monster with DR/- doesn't get any DR penetration ability because of it's DR. Their attacks don't count as magic, or of any material.

Certain massive monsters (Rolling out the Tyrannosaurus again) have no DR at all, but are massive beasties; do their attacks not count in any way against DR? (Not that the T-Rex needs to worry much about DR, it does massive amounts of damage!)

7) Nope. Their attacks do lots of damage, for sure, but they have no special DR penetration.

Spells aren't affected by DR at all? So your common or garden magic missile happily does full damage against a monster with 20/- reduction?

8) Correct. Specifically:

Spells, spell-like abilities, and energy attacks (even nonmagical fire) ignore damage reduction.

One of the things that you keep mentioning is alignment and material DR being equivalent to certain enhancement bonuses. All that table says is that weapons with a high enough enhancement bonus let you bypass certain types of DR. Being able to bypass aligned DR does not make your attack equivalent to a +5 weapon. Being able to bypass aligned DR does not let you also bypass silver, adamantine, and magic for free. The specific rule to pay attention to reads:

Weapons with an enhancement bonus of +3 or greater can ignore some types of damage reduction, regardless of their actual material or alignment.

This only applies to weapons with a high enough enhancement bonus, not any other attacks that can bypass certain types of DR. Note that this does not apply to weapons with a high effective enhancement bonus, only a high actual enhancement bonus. The rules for enchanted weapons state:

Special abilities count as additional bonuses for determining the market value of the item, but do not modify attack or damage bonuses (except where specifically noted).

Since the enhancement bonus to DR rules only mention enhancement bonus, and don't specifically call out that the full effective enhancement bonus applies, only the actual enhancement bonus applies.

Another thing to keep in mind is that creatures with an alignment subtype apply their alignment to their weapons as well as their natural attacks, while creatures with DR/magic only bypass DR/magic with their natural weapons.