Is there a limit to the size of a family file I can put on the iPhone?
Reunion does not impose a limitation on the family file size or number of people.
Most features (like navigating from one person to another, editing data, adding new names, etc.) are not affected by the size of the family file.
The main feature that will become slower with large numbers of people is the People list and the Places list. Performance in these lists will degrade in family files exceeding approximately 6,000 people. The processor in the iPhone is not nearly as fast as the processor in your Mac.
If you have a very large family file, one work-around is to use the Find feature. I.e. you can search for a particular person or last name instead of opening the Index with the entire list of names.
Perhaps the best work-around is to send a marked subset of your family file to the iPhone, rather than the entire family file. For example, you can use the Mark > Mark Groups feature in Reunion for Macintosh to mark a subset group of individuals in your family file and upload them to the iPhone. Information about using the Mark Groups feature can be found by searching your Reunion for Mac manual for "mark groups" (without the quotes).
Of course, you can try uploading your entire family file and see if the speed of the People List is a problem for you. The file on the iPhone can be deleted if you are not happy with the performance.