Sunbird's invocation implied rules
Does it mean spells with {X} sometimes have CMC 0 and sometimes X?


Yes, but thankfully it's simple:


If a spell is on the stack, {X} is treated as the value the caster chose for it.
Anywhere else, {X} is 0.


This comes from comprehensive rule 202:


  202.3d When calculating the converted mana cost of an object with an {X} in its mana cost, X is treated as 0 while the object is not on the stack, and X is treated as the number chosen for it while the object is on the stack.


However, the second ruling is referencing something else entirely: if you cast a card "without paying its mana cost", you always have to choose 0 for the value of {X}. You're not paying its mana, so you don't get to pick some other arbitrarily value. This means, more often than not, it is not worthwhile casting an {X} spell for free.


  Additionnaly, can I play a land from the revealed cards?


No. Sunbird's Invocation says you cast the card. Lands can't be cast, only played. See Stromkirk Occultist for an example of a card that lets you play lands.