The first concerns the theory of syntax and grammar that typologists prefer:
What theory of syntax and grammar do language typologists tend to prefer? Do they prefer a transformational phrase structure grammar of the sort that was prevalent in the 1970s, or do they prefer more modern minimalist theory? Or perhaps they prefer dependency grammar as opposed to phrase structure grammar?
The second concerns the apparatus they assume to address specific word order questions:
How do typologists approach basic questions about the theory of word order? Consider, for instance, the placement of attributive adjectives (e.g. big house vs. *house big). Germanic languages tend to place the adjective before the noun, whereas Romance languages tend to place it after the noun. How do language typologists address this difference? I assume they address it in terms of heads and dependents, but then what is the basic understanding of heads and dependents that they start with?