I have an SQLite3 database which has 8 tables and in which data will not change so needs no add option.
Each table has 4 or 5 fields of different types.
In order to use this data in an Android app I need to load it into spinners.
My questions are:
1. Is it best to keep and work with database in Assets folder or load details into arraylist? (How would I separate fields)?
2. How do I load data into one spinner depending on input in the other and can I choose either spinner first.
EG. If I choose last names could all possible first names be loaded into second spinner and if I choose first names could all possible last names be loaded into second spinner?

I think the amount of data and how you need to interact with it should be the deciding factor. The avantage of databases is that selecting the information is easy, depending how complex your data is this may not be the case for an array.
The answer to your second question is yes, either storage method will allow you to do that but, again, the database will be easier to deal with and probably involve less code.