have had her since 2004 and so far so good, we are very happy with her. She has been quite low maintenance but with age has become a little snappy around kids visiting our home, but no issue for our own kids or kids that are known to the family. We got her when she was about 5 weeks old and just weaned.
Farm dogs need to be given a very good cleaning and deworming. Check very carefully for insects in the ears and on the skin.
We were able to register her no problems.
Before you opt out of applying for a Finnish passport you should check if you can get your child onto your wife's Hukou, if you can't do that then your kid will be considered as an 'unregistered' citizen and wont get a place in a local school for free anyway or be able to apply for a Chinese passport.
Most people I know that are in your situation apply for the child's foreign passport, the child doesn't need a visa to live in China as the Chinese consider a child with at least one Chinese parents to be Chinese.
Each time you leave China you will need an exit permit for the kid which is easy and quick for your wife to apply for and is shown together with the foreign passport to leave and get back into China.
Parents of foreign kids that I know of pay about 20k rmb a year for a local school, but as your kid would be technically a Chinese citizen, even without a hukou it would probably be cheaper.
Ask your wife to check the cost at a local school near you for reference.
when we renovated we took our workmen to B&Q to select materials from their excellent range if samples. Then with that list in hand we went to the construction market near Mingbo bridge and got the same materials at either half or one third of the B&Q price.