There’s no way that I know of to get access to the full Milltown records without paying.
Some of the Milltown records are on the UHF site but you have to pay for that. See:
Findagrave has them too, but that’s a pay to view site.
I don’t have an e-mail address for Milltown but their phone number is 028 9061 3972. They will search for a plot number free, but if you want to know who else is in the grave, there’s a £20 charge.
For school attendance records, PRONI has most of the surviving records. They have quite a lot for Belfast. You need to know which school the pupil attended though. I should they think they have about 100 sets of records for Belfast schools. (The list is on the PRONI website).
St Patrick’s baptism records for the 1860s are on the NLI website. There is a gap between 1867 and 1875 though. St Mary’s are there too from 1867 up to 1881. (Their earlier records are lost).