As I understand it, radar data collection will begin when the
periapsis drifts into the night hemisphere and the ionosphere becomes
quieter at close approach. This will take several months, by which
time the periapsis will be in the southern hemisphere.

Radar data cannot usefully be detected in the daytime due to the active ionosphere, so there will be some tests of the radar and then some probing of the properties of the ionosphere while daytime data collection activities continue (mostly cameras).

Unfortunately, there wasn't enough fuel to circularise into a low orbit, and ESA isn't brave enough to do long-term aerobraking like NASA do these days. (and a 40m radar antenna is a bit vulnerable in those circumstances)

There is info on this topic on the Mars Express website, but very
poorly indexed - you have to dig for it. Look at what you can find on
MARSIS, eventually it'll tell you the orbit plan.