I need to create a lot of points with lots of attributes, but most of the fields are the same, so I don't want to edit all the fields all the time. Is there a "remember previous fields" function available?
In QGIS, try
Settings -> Options, Digitizing tab:
Feature creation [x] Reuse last entered attribute values.
This works for newly created objects, but not if you fill in data of already existing objects.
Could you make use of the Quick Multi Attribute Edit plugin? You can create a number of points first, select a group of them, and bulk edit common attributes using the plugin.
If you are entering house number points please also try the house numbering qgis plugin: