Both claims are FALSE



1
The moon's orbit is continually getting farther from Earth and has been doing so since its capture/formation.

2
The "spin" of the Earth has speeded up ever so little. One cause was the massive ocean floor collapse that created the giant sunami.
Like a spinning figure skater who brings in her arms a bit, the spin will accelerate.

As regards to the orbital speed of the Earth around the Sun... I do not have the current data so I do not know.