Generally no. They are usually private records, and access depends on the congregation's or archive's policies.
Often in a regional or denominational archive. Some have also been microfilmed or digitized and are available through libraries.
Not necessarily. Baptism or naming may occur weeks, months or years after birth, so compare with civil birth records.
Transcribe carefully, mark uncertain readings and ask the archive or someone familiar with the tradition for help with terms and abbreviations.
Use only what your research requires and avoid publishing private family details that do not bear on the case.