Though your questions are certainly worth mentioning, I can only speak for the Church I attend.
Admittance to the Lords Table in the Church I attend is based on confession of faith, not on whether someone is baptized or not. The applicable Scriptural warning of taking the Lord's Supper in an inappropriate manner are read every time we celebrate the Lord's supper.
The elders of the Church are actively lovingly involved in the lives of all attenders, regardless of whether they are members or not. This is understood by all and is not optional, for anyone who attends.
Tom