The Egyptian military doesn’t need US aid to launch a coup. Sure the military will have made sure that the US continues to consider Egypt as an ally but that’s about it. Politically both are taking potshots at each other.

Mursi was democratically elected, yes. Quoting Wikipedia:

Within a short period, serious public opposition developed to President Morsi. In late November 2012, he issued a temporary constitutional declaration granting himself the power to legislate without judicial oversight or review of his acts, on the grounds that he needed to “protect” the nation from the Mubarak-era power structure. He also put a draft constitution to a referendum that opponents complained was “an Islamist coup”. These issues — and concerns over the prosecutions of journalists, the unleashing of pro-Brotherhood gangs on nonviolent demonstrators; the continuation of military trials; and new laws that permitted detention without judicial review for up to 30 days, and impunity given to Islamist radical attacks on Christians and other minorities — brought hundreds of thousands of protesters to the streets starting in November 2012. During Morsi’s year-long rule there were 9,000 protests and strikes.

Is Sisi a champion of democracy? No. But also he was elected, and he’s legitimately popular. Morsi rode to power on an illusion about Brotherhood politics, once they unveiled their true colours Egyptians quickly decided that they’d rather have secular than religious authoritarians in power.