Retraction is the main factor in why prints will have small strings of filament between open spaces. When the nozzle head moves over open space of the bed to go to another portion of the print, the printer will retract or back the filament away from the hot end. This setting can be found in your 3D printing software and, if you are having issues with stringing, you can increase the retraction distance and speed. Be careful to not make this setting too high as it can cause issues like filament grinding.
The temperature of the nozzle can also play a role here. If the nozzle is set too high while the printer head moves between open space, the nozzle may actually allow filament to drip out into the build space. You can fix this issue by lowering the extruder temperature. Keep in mind that a temperature too low can cause a clogged nozzle and filament grinding.
If your print is moving too quickly from point-to-point, it can cause the filament to drag and cause overhang. What happens is the filament does not have time to set and stick to the previous layers, causing the portion of the layer to drag outside of the build space. You can change these settings in the printing software under movement speed.
Why is the infill "stringy"?
The main culprit for the internal supports of your print being stringy would be the thickness of the layers put down into the infill. You can increase this setting in Cura under Fill settings.
The most common issue with infill is the infill speed being set too high. This is normally fine because no one will see the infill, but it can cause problems for the surrounding edges and structural support. You can change this setting in Cura under the Advance tab and Speed category.