Let's evaluate the chemical reactions mentioned in the statements to determine their accuracy.
Analysis of Statement I:
1. Decarboxylation of sodium ethanoate: When sodium ethanoate ($CH_3COONa$) is heated with soda lime ($NaOH$ and $CaO$), it undergoes decarboxylation to produce methane. The reaction is:
$$CH_3COONa + NaOH \xrightarrow{CaO, \Delta} CH_4 + Na_2CO_3$$
This part is correct.
2. Kolbe's electrolysis of sodium acetate: In this process, an aqueous solution of sodium acetate ($CH_3COONa$) is electrolyzed. At the anode, acetate ions lose electrons to form methyl radicals, which then combine to form ethane ($C_2H_6$), not methane. The reaction is:
$$2CH_3COONa + 2H_2O \rightarrow C_2H_6 + 2CO_2 + H_2 + 2NaOH$$
Since this method produces ethane, the statement's claim that it prepares methane is incorrect.
3. Reaction of $CH_3MgBr$ with water: Methyl magnesium bromide is a Grignard reagent. It reacts with water (a source of protons) to form methane. The reaction is:
$$CH_3MgBr + H_2O \rightarrow CH_4 + Mg(OH)Br$$
This part is correct. However, because the Kolbe's electrolysis part is false, Statement I as a whole is False.
Analysis of Statement II:
1. Preparation from unsaturated hydrocarbons: Methane ($CH_4$) contains only one carbon atom. The simplest unsaturated hydrocarbons (alkenes or alkynes) must have at least two carbon atoms (e.g., ethene $C_2H_4$). Standard hydrogenation of these compounds results in alkanes with the same number of carbons (e.g., ethane). There is no direct standard preparation of methane from unsaturated hydrocarbons. Thus, this part is correct.
2. Wurtz reaction: This reaction involves the coupling of two alkyl halides in the presence of sodium to form a higher alkane ($2RX + 2Na \rightarrow R-R + 2NaX$). The smallest possible product, starting from methyl halides, is ethane ($C_2H_6$). Methane cannot be synthesized this way because it only has one carbon. This part is also correct.
Therefore, Statement II is True.
Conclusion: Statement I is false and Statement II is true.