I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 20 M church/civil/census B/M/D records for MOST Irish counties, including Donegal. Records before 1863 are increasingly sparse - almost non-existant by 1800. Protestant records are the LEAST likely to have survived.
1. For Mary McMonagle B 1850 +/- 5 yrs, Co. Donegal, with the parents' names unknown, I found 1 record: 1851. A view of the detailed record (at a small fee) SHOULD show the parents' names and other info
2. For a Mary McMonagle and Dan(iel) Sweeney marriage 1869 +/- 2 yrs, Co. Donegal, I found 0 records.
3. For Daniel Sweeney B 1848 ditto, with a father forenamed Bernard and mother Sarah Breslin, I found 0 records.
Regarding 2. Civil B/M/D registration was mandatory after 1863. Civil records are more likely to have survived. They SHOULD be in the above database. Civil records are kept by the General Register Office. Query it at GROIRELAND.IE. Fees may apply.