State of a Racemic Mixture
Is a Racemic Mixture always an equi-molar solution of two enantiomers, both in the same state?


Yes and yes. A racemic mixture is equimolar in both enantiomers. Otherwise you would call the reaction enantioselective with a so-and-so selectivity.
A racemic mixture contains both enantiomers in the same state, as energy differences between enantiomers are so minuscule that you would never get one solid and one liquid at the same time.


  Is it necessary for both the mixture to be liquid in nature, or does racemisation also occur in the gaseous or solid state?


Racemisation is the process where you start out with a pure enantiomer and in the end get a mixture. For complete racemisation you end up with an equimolar mixture as discussed above.

It is thus possible that racemisation occurs in gaseous and solid phases, not only in solution or liquid. However, the reaction times will differ significantly. I could imagine that the solid racemisation reaction will take a long time.


  Can the two enantiomers still form a Racemic mixture if they are initially at different temperatures?


Higher temperatures just mean that the racemisation process proceeds faster. In the end, the warmer enantiomer will have racemised further on than the colder one, but for $t\to\infty$ the result will be the same.