Step 1: Understand the nature of phenoxide ion.
Phenoxide ion is formed by removal of a proton from phenol.
\[
C_6H_5OH \rightarrow C_6H_5O^- + H^+
\]
The negative charge on oxygen is delocalized over the aromatic ring through resonance.
Step 2: Understand O-alkylation.
In less protic solvents such as ethers, the oxygen atom of phenoxide ion remains highly nucleophilic. Therefore, alkylation generally occurs at oxygen leading to O-alkylation and formation of ethers.
Hence, statement (A) is true.
Step 3: Understand behavior in trifluoroethanol.
Trifluoroethanol is a strongly hydrogen-bond donating solvent. It strongly solvates the oxygen atom of phenoxide ion and decreases its nucleophilicity at oxygen.
As a result, nucleophilic attack through the aromatic carbon becomes relatively favored, leading to enhanced C-alkylation.
Hence, statement (B) is true.
Step 4: Analyze statement about ethers.
Ethers are poor hydrogen bond donors because they do not contain acidic hydrogen atoms. Therefore, ethers cannot form strong hydrogen bonds with phenoxide oxygen to improve solvation.
Hence, statement (C) is false.
Step 5: Analyze aromatic conjugation during C-alkylation.
C-alkylation of phenoxide ions occurs at ortho or para positions while preserving aromaticity and resonance stabilization of the benzene ring.
Thus, aromatic conjugation is not disrupted.
Hence, statement (D) is false.
Step 6: Identify the correct statements.
The true statements are:
\[
(A) \text{ and } (B)
\]
Step 7: Final conclusion.
Therefore, the correct answer is
\[
\boxed{(A)\text{ and }(B)}
\]