Actually, In Mandarin, tones 1 and 2 are 平声; they are 阴平 and 阳平, respectively, and represent a split in the older, single 平声. Tones 3 and 4 are 仄声; they are 上声 and 去声, respectively. The 入声 (the entering tone) no longer exists in modern Mandarin; it is distributed among the other tones. This fact, and the split in the 平声, means that the 平仄 rules for poetry behave differently in modern and classical contexts.

Yes. AFAIK if a tone is not a 平聲, then it is a 仄聲 (including 上聲, 去聲, and 入聲). For example, in Mandarin tone 1 is 平聲, tones 2, 3 and 4 are 仄聲. In Cantonese, tones 1 and 4 are 平聲, tones 2, 3 and 5 to 9 are 仄聲.