It would take about 175,000,000,000 (175 billion) years to get to the Andromeda galaxy! So, no. We haven’t, it’s useless. read more
We have not yet sent a probe outside our own Solar system (which, compared to the Galaxy, is microscopic). The furthest object we have sent is at roughly 113 astronomical units from the Sun (Earth's orbit is at one astronomical unit). read more