Hmmm for someone wanting 'to only communicate by text' she is doing an awful lot of phoning . Go with the flow for now, unless it is an issue you need to set a boundary on.
I think you took her by surprise by the phone thing! That is always good. It looks like she got the phone anyway so at least you are not the bad guy eh? It was great that it enabled you to engage in discussion rather than deadlock and it has appeased you somewhat in your suspicians as to why.
On the positives, there is nothing more hideous than having to talk girl stuff with your dad so maybe that is a good thing. Remember, don't take it personally it isn't always about you (which btw I am totally guilty of doing most of the time so taking a huge spoonful of my own medicine!).
No harm in texting her and saying 'btw thank you for the DVDs and smoothie maker'. I'm interested to know why you didn't say thanks at the time... are you sure you didn't? It is automatic for me to say 'yes, thanks' or 'yes, thanks for doing that, much appreciated'.
. Go with the flow for now, unless it is an issue you need to set a boundary on. 
