“表明” is a verb. It means someone indicate his/her attitude ，point and suggestion. You could use some nouns as its object, such as “立场，意见，看法，观点” etc.
Ex. , 他表明了他的立场。这件事表明了大众的看法。
“表情” is a noun. It means the feelings express on a person's face. It should not be used as a verb or other categories of words.
“表示” can be used as a verb or a noun. When it is a verb, it means someone show his/her attitude , feeling and emotion. It can replace “表明” in a few situation. Be carefully, The subject of “表示” is human , human group or some intelligent things.
Ex. 他表示很开心。 学校领导表示愿意和企业合作。
When it is a noun （usually in oral Mandarin）, it means someone should do something or show his attitude to someone. It is hard to express in language.
“表现” is a verb or a noun. It means someone show his/her thought or advantages. You could use some nouns as its object, such as “犹豫，果断，优点” etc.
When it is a noun, it means someone's performance in an event.
“表演”is a verb or a noun. When it used as a verb. It means someone perform an act of play, music or some kinds of entertainment.
When it is a noun, it means an act or a show. Sometimes it is a metaphor that means someone's action in an event .
Hope it could help.