SARS-CoV-2 is a major threat to global health. Here, we investigate the RNA structure and RNA-RNA interactions of wildtype (WT) and a mutant (Δ382) SARS-CoV-2 in cells using Illumina and Nanopore platforms. We identify twelve potentially functional structural elements within the SARS-CoV-2 genome, observe that subgenomic RNAs can form different structures, and that WT and Δ382 virus genomes fold differently. Proximity ligation sequencing identify hundreds of RNA-RNA interactions within the virus genome and between the virus and host RNAs. SARS-CoV-2 genome binds strongly to mitochondrial and small nucleolar RNAs and is extensively 2'-O-methylated. 2'-O-methylation sites are enriched in viral untranslated regions, associated with increased virus pair-wise interactions, and are decreased in host mRNAs upon virus infection, suggesting that the virus sequesters methylation machinery from host RNAs towards its genome. These studies deepen our understanding of the molecular and cellular basis of SARS-CoV-2 pathogenicity and provide a platform for targeted therapy.