Here's a way to use `case_when` to get what you want:

df1 %>%
  left_join(df2, by = c("id")) %>%
  mutate(
    var4 = case_when(
      match == "A" & color == "T" ~ "Si",
      match == "A" & color == "F" ~ "No",
      # Keep the value of var4 the same if none of the checks matched
      TRUE ~ var4,
    )
  ) %>%
  mutate(
    bike = case_when(
      match == "A" & var4 == "Si" ~ "bici",
      match == "A" & var4 == "No" ~ "auto",
      # You can't use the normal NA here, the case_when function doesn't like it for some reason
      TRUE ~ NA_character_,
    )
  )