Olsen/Olsdatter just means son or daughter of an Ole - that is the most common name in all of Norway, and doesn`t necessarily indicate and relationship.
The Thomas Olsen you found at Oxaas in 1801 would have been 80 years old when Anne T. was born, not a likely father.
The 1865-census for Andreas OLS. is just a misprint.
The wife of Andreas Anders. brother Ernts Anders., Pauline Olsdtr., she could of course be a sibling of T. Olsen/Olausen/Oluffsen, but that would take some proving.
The Ingeborg Knutsdtr. you found in Kviteseid is not yours. Kviteseid-Ingeborg is married and has children with Aane Olafsen, and Kviteseid is far from where Kari Pedersdtr. was born! Kari P`s mother Ingeborg is born abt 1833, in (Østre) Slidre.
Here is your Ingeborg in 1865: http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=visbas...
There are a couple of candidates for her there, the best candidate I have found so far was christened 16 Feb 1833 daughter of Knud Knudsen and Marit Jonsdtr. (Ingeborg`s first daughter named after her husbands mother, her second daughter named after her own mother, which was custom). I have yet to find a farmname for the parents, they seem to be dead by 1865.