I'm used to being able to go into a slicer and specify an amount of fill, load up more than 1 part on a plate, etc. (think slic3r).
Is there any way I can get to some of these details?
You can do all of these and much more via the Polar Cloud (https://polar3d.com). I'm going to assume, therefore, that you are looking at the local web interface on the printer itself? The one in which you can load an STL or a gcode file and tell it to print BUT specify no slicer settings.... Yes, you cannot do much from that "local" web interface. We likely, in the Fall or Winter be adding some additional capabilities to that local web interface but likely not as much as you are looking for (e.g., control slicer settings and position the model on the build plate).
For more sophisticated control, use the Polar Cloud. From there you can load multiple models to the build plate from a number of sources: your collection of objects, shared or public objects, your local file system, or even Google Drive or BlocksCAD (https://www.blockscad3d.com). You have full control over all the Cura slicer settings (and there's plenty of them). Once the print job is queued to a printer, you can edit it adding/removing additional models from the build plate. You can even combine one or more queued print jobs into a single print. And once a print is finished, you can revisit it in your listings of past prints. That allows you to requeue the print using the same slicer settings as it printed with before (or you can change them).
Also, via the Polar Cloud, the printer can be shared with other users allowing them to queue prints to the printer as well. You have control over the level of access they have. E.g., they can queue to the printer and view the printer (via its camera). Or they can have limited management (see the entire queue and start and stop jobs). That's done by sharing the printer with a group and giving the group that level of control. And, finally, you can make other cloud members managers of the printer thereby giving them more complete control of the printer and its queue.
Anyhow, I hope that actually answered your request!
If you queue a print job, you can then download the slicer settings from the print job. You can use those settings as a guide to setting up your Cura profile. Unfortunately, Cura has changed more than once their format for slicer settings. We do not attempt to keep track of those changes, some of which have been pretty radical.
To download the slicing config, just queue a print job. Then, on the printer's dashboard page, locate the "tile" for the job in the displayed queue of jobs. Click on the three vertical dots in the upper right corner of the tile. Then, in the menu which appears, select "Download Config File". That will download to your computer a file named X-config.ini where "X" is some random string. This .ini file is a CuraEngine .ini file with all the slicer settings. That .ini file is what Cura feeds to its slicing engine, CuraEngine.