Here below I included an informative article on how Georgia got to this place of audit and hand recount:
Note in here a new law passed in Georgia in 2019 that gave its Secretary of State discretion to audit any one election with emphasis on oversight for new voting machines/technology being installed in time for this November 3rd cycle.
In addition, although close elections do not automatically mandate a hand recount in Georgia, any candidate trailing by less than 1/2 of 1% of the total population/voter roll will be granted it upon request.
Regarding your 2nd question, Trump like any sitting POTUS currently has access to emergency powers contained in 123 statutory provisions, as recently calculated by the Brennan Center for Justice at NYU School of Law. On their website, their is an interesting article by Elizabeth Goitein dated December 12, 2018 highlighting that any President could most certainly declare this or any general election a national emergency at his or hers sole discretion.
One example cited was with the flick of Trump’s pen, certain laws can be activated allowing him to shut down many kinds of electronic communications inside the United States or freeze American bank accounts.
I imagine that Trump could shut down/take over tweeter, google and face book immediately.
Also could freeze monies sitting in the Democratic Party and PAC initiatives too.
Other powers are available even without a declaration of emergency, including laws that allow the president to deploy troops inside the country to subdue domestic unrest.
Esper, the Defense Secretary was fired last week. A clue that if any streets return to rioting, Trump is perfectly within his rights to bring in the militia to quell violence.
So, the authority here for a sitting President here are pretty clear.
Courts could still rule if petitioned that such acts evoked are unlawful or not constitutional.