I can make sense of the summaries and introductions, but that is all.
That is a problem. If you are so unfamiliar with the field that you cannot understand anything about the methods, how can you know if this is what you want to do for the next 5-6 years? A certain amount of training is expected to happen during a PhD but graduate school is not like undergrad. There are no TAs. Great majority of PIs do not have the time to hold your hand and teach you everything. You need to seriously consider if you have the necessary background to do a PhD in this field.
Do supervisors ask applicants about whether they have read their papers?
They will ask why you want to join their lab. If the plan is to say "I haven't seen your work but XYZ", XYZ better be good!
Do I attempt to summarise vaguely what the paper is about?
You could try asking a question about the paper. You probably should admit straight away that you don't understand the methodology very well. Perhaps the PI will be willing to explain it to you! (This actually happened to me several times, most scientists are very eager to talk about their research)
What sort of questions may be asked about papers?
Future directions, next experiments to do, etc are popular questions since that is exactly what you would be doing if you joined the lab.
Can you just say something along the lines of ' I find it very interesting that you did a recent article in ????' for flattery?
You can but you will likely be asked what you like about the article.
NOTE: I am a biomedical researcher, not a physicist.