1. Synthesis of Sodium Acetate (CH₃COONa):

   • It can be obtained, for example, from acetic acid (CH₃COOH) and sodium hydroxide (NaOH):
     [ CH₃COOH + NaOH -> CH₃COONa + H₂O ]

2. Synthesis of Sodium Hydroxide (NaOH):

   • Usually produced industrially, for instance, by electrolysis of a sodium chloride (NaCl) solution:
     [ 2H₂O + 2NaCl -> 2NaOH + H₂↑ + Cl₂↑ ]

3. Dumas Reaction (producing methane from sodium acetate):

   • Using sodium acetate and sodium hydroxide to produce methane:
     [ CH₃COONa + NaOH -> CH₄ + Na₂CO₃ ]
     The reaction temperature varies from 300 to 400 degrees Celsius

The first two are already features (the second one being 'catalysed' by mercury). I'll look into the Dumas reaction.

The sodium amalgam produced by the ingame Castner-Kellner process
only contains a pitiful 0.00045 M of Sodium, with doesn't even show up in the JEI tooltip (just saying 0.00 M instead)

Good point. That's been fixed in 0.4.

I wonder if electrolysis releases gases, how to collect them from the basin?

Since the hydrolysis of sodium chloride releases hydrogen gas and chlorine

The inability to handle gases in Basins is an intentional limitation. They just evaporate. In future versions, electrolysis will probably be possible with a Vat (or pair of Vats). Bear in mind that for this implementation of the Castner process specifically, a solution of chlorine is produced, which is not gaseous.

Adding on to this, is alkali-catalyzed decarboxylation general enough that it should be applicable to all carboxylic acids? I know that you can make benzene by an alkali-catalyzed decarboxylation of benzoic acid.

Decarboxylation by hydroxide is not super common. Some sort of generic decarboxylation will probably be added in the future, though not by hydroxide.