About English: Some of your complaints have been fixed. Other examples are idiomatic to mathematics writing, and hence may not be fixed.
About jargon: Mathematics, like any highly technical field, has its own jargon, which does not appear in non-mathematical dictionaries. Part of the function of Wikipedia is to explain and exemplify jargon for readers, so that they can understand other texts that use such jargon.
About difficulty: This is a common complaint about mathematics articles on Wikipedia. (See FAQ at the top of the project talk page here.) This Projective plane article is not a bad offender, in comparison to many other articles. It attempts to give visual intuition, historical context, applications, etc. The later parts of the article are more obscure, but only highly motivated readers will attempt those anyway. Fundamentally, this is an article about a moderately advanced mathematical topic, that few non-mathematical laymen ever encounter. So the difficulty seems about right to me. Yes, there is always room for small improvements, but no dramatic change in tone, organization, content, etc. is warranted.