"Security Against Covert Adversaries" question
1) $x_0$ is (indeed) a plaintext. (Perhaps to guess at where confusion arose from:) the 'more modern' version of homomorphic encryption is fully homomorphic encryption (FHE) fully supporting both additive and multiplicative homomorphisms, whereas the paper you're reading was published about 2.5 years before Gentry's original FHE scheme came out. (Check out the wikipedia article on homomorphic encryption for more examples..)

This paper uses additive-homomorphic encryption, which allows the computation $Enc(pk, x_0) + Enc(pk, x_1) = Enc(pk, x_0 + x_1)$. Note that additive-homomorphic encryption schemes tend to support (must.. support?) an additional "scalar-multiplication homomorphism." That is, the computation
$$x_0 \cdot Enc(pk, x_1) = Enc(pk, x_0\cdot x_1),$$
where plaintext $x_0$ is public information.

(Note that the above is different than FHE, which supports both the prior additive homomorphism, and simultaneously the "full" multiplicative homomorphism of $Enc(pk, x_0) \cdot Enc(pk, x_1) = Enc(pk, x_0\cdot x_1).$)



2) Read it as a field =)