Needing some transcription help

[Lynn Christiansen]

I have located the Birth entry for a 4th Great Grandaunt--Maren Jensdatter Faxholm at the Danish Staten Archive 1770-1815 Kalundborg Vor Frue, Ars, Holbæk img 23 pg 30- #30
 
https://www.sa.dk/ao-soegesider/da/billedviser?bsid=474596#474596,84626911

My transcription attempt is:
Year: 1772
Numb: 30
Left Margin Note: Introduceret d 17 p Trinit
Details: Dom 11 p Trinti d 30 Aug, Jens Christensen Fazholm og kone Martha Maria Hansdtr en Daatter til Baaben, kaldet ... MAREN født Tirsdagen af 25 ??? Catrine Nielsdtr paa Kierutf basr barner og Birthe Christensdtr paa Crragsten (?)  ??..?? Fadderen waren Monsr Fritz paa Teilberg; Hans Johan Gieritings Søn; Birgitte Splittoft og Ane Jenssdtr paa Kiriten Blank

I would appreciate someone reviewing it for accuracy and make the needed corrections as necessary.


I also found what I believe is her Death entry located at Danish Family Search at: 1824-1834 Kalundborg Vor Frue, Ars, Holbæk img 319 pg 223-#26

https://www.danishfamilysearch.com/sogn451/churchbook/source141827/opslag15747624

My transcription of this is:
Year: 1829
Numb: 26
Death date: 10 December
Burial date: 14de Decembr
Name: Maren Finstad fød Faxholm
Status: Kløbmd og Madtsaustmand Finstad hust (?)
Age: 57
Index 243
Remarks: do (ditto- ???)

Here I need help with her Married name and the in Status column, the comments (I believe they related to her husband) and finally, the Remarks section.

Thank you for any assistance.

[Grethe Leerbech]

Dom 11p Trinit d. 30 Aug Jens Christensen Faxhholm og kone Martha Maria Hansdtr en Datter til Daaben, kaldet Maren
født Torsdagen d 25 Hujus (latin for hujus mensis means this month )
Cathrine Nielsdtr hos Kierulf bar Barnet og Birthe Christensdtr hos Prousten stod hos
Fadderne vare: Monsr. Fritz paa Teilberg, Hans Johan Gierstings Søn, Birgitte Splittoft og Ane Jensdtr hos Kirsten Blank

bar barnet- carried the child, stod hos - stand besides them*,  prousten- the priest, another name for priest
Fadderne vare - the faders were:
paa - at and hos - by

* she was often the woman who carried the childs small bonnet.

 

The death entry:

Maren Finstad fød Faxholm
Kjøbm. og Stadthauptmand Finstads Hustru
57 år, index 243 (jvfr. register)
bemærkninger: Begrv paa Olai Krkgrd. 

Maren is called Finstad, fød means born
ed as you also write. Her husband Finstad is a grocer and citymayer. He could also be a merchant, its not clear, the word købmand could mean both
the remarks say she is buried at Olai churchyard 
 
   

[Lynn Christiansen]

Thank you for the quick response...