People who have been slowed down by her semblance won't have the feeling of being slowed down but there are some indications that her semblance is active. A bright yellow glow surrounds her when she activates her semblance as well as the sound of a clock ticking.
I'm assuming the savaging program can act as a Co-op program through the school allowing Dorothy to complete her training and become a hunter while also savaging and treasure hunting.
If a projectile leaves Dorothy's hand while she has her semblance activated it will leave her aura and become affected by the slow that is in place at the time (moving slowly in 1, very slowly in 2 and nearly suspended in 3). When Dorothy activated her semblance in relativity to the normal world she is going extremely fast. However her punches and blows still do the same amount of damage that they would do in normal time.
she is simply moving through time fast enough that it's essentially slowing it down
Interesting fact: Dorothy can use the semblance in a reverse way as well. Time around her slips past her at amazing speeds while she seems to slow down her existence to a crawl. This doesn't have any combat functionality but it does help to pass the time in the hospital after abusing her semblance too much.