No - keep exporting them as sRGB jpegs - that's the only colour space available for jpegs
Not true.
and sRGB is also the colour space of most computer monitors/displays.
Also not true and for two reasons.
1) ICC specified RGB Color Spaces are sets of device independent values describing how the numbers that make up color in the digital world color values are and the limits for . I won't go into the details but the important thing to note is that ICC specified color spaces such as sRGB, Adobe RGB(1998), and Pro Photo RGB are device independent sets of abstract values.
1) A display is a device, a very specific device with innate characteristics and limitations as to how it reproduces color. This is why it is advisable to use a colorimeter or photospectrometer and its related software to characterize ( otherwise known as calibrating and profiling) a display so that corrections can be made to the signal the video /graphics processor is sending to the display that adjusts the signal to compensate for those characteristics. While a device's RGB profile is a type of colro space, it only describes a very specific, unique way of reproducing color values.
While many manufacturers say their displays are "sRGB" what that only means is that the gamut (palette) of the device is large enough to contain the gamut described by the sRGB specification.