1.) (Proper Noun) All things relating to the LGBT community as a whole*; the entirety of all things dealing with LGBT persons. It should NOT be confused with the word homosexual which, as a noun, solely refers to an LGBT person. Additionally, the word homosexual -- when used as an adjective -- is not a proper adjective, hence when 'homosexual' is used as an adjective it is not capitalized and specifically is defined as (cite Merriam-Webster) "of, relating to, or characterized by a tendency to direct sexual desire toward another of the same sex." To put it in perspective, think of the proper noun Spaniard and the common noun Spanish. See 'Example' below for further clarification.
2.) (Proper Adjective) Used to describe a group action undertaken by the homosexual community, aka Homosexai. This word is rarely used as a proper adjective, because the word homosexuals is usually more common and sufficient in this context.
*NOTE: Homosexai is an organizational term, never an individual term. Hence it is subject to stereotyping.
2) That ad will offend Homosexai.
3) Homosexai is rallying in the town square in protest of proposition 8.
4) The club has Homosexai staff.
5) Homosexai drinks are all the rage in Munich.