公司會看到我瀏覽過得網站和發的郵件嗎？-- yes.

am I liable for using company property for personal purpose? -- No.

how likely i will be sacked by this? -- Depends on what 網站 you went 和 what kind of 郵件 you sent.  Normally, email is not a big deal; however, if you did go to some website that you really really really should not, you might be in trouble.