True that the Bible doesn't use the term "trinity" but if one does study the Bible, especially in the New Testament you will find some obvious referrals to the existence of "a Trinity". Here are two instances:
Most notable is the command of how to baptize someone (Mt 28:19) and the original Greek use of "name" is singular. If it is singular then how can anyone otherwise interpret the 3 names as less than belonging to one person (God)? Not a Greek scholar but I do read the writings of those with that training.
Matt. 3:16-17 describes the descent of the Holy Spirit onto Jesus as he was being baptized. The voice of God was heard at the same moment so that shows "3". And I can't adequately describe the process of 3 in 1 other than saying each of us holds different roles in our lives and that is as close as I can to giving an example of 3 in 1 (for example I am the son of....the husband of....the father of.....).
As for any religion being a meld of others, so what? Truly what does it matter in the scheme of things? If I choose to commune with my God and feel that communion is doing something positive in my life then who is to criticize me? On what basis? Now as for the issue of those with the quoting of some other religions, that is what one can expect to see if the school system decides to go off onto something without getting parents involved. I believe, strongly, in the role of parents in the education of their children. When that child grows and enters the world (figurative term) then what the world decides to show the child will be compared to what they learned as a child, either for better or worse. The way it has always been and the way it will always be regardless of the rantings of a vocal group.