Does President Trump Have a Neurological Problem?

President Trump spoke to graduating cadets at West Point on June 13, 2020.  During the speech, he sipped from a cup of water.  He held the cup in his right hand, but apparently couldn't lift it all the way to his lips.  He then used his left hand to lift the cup all the way and drink. (See the video at https://twitter.com/atrupar/status/1271820635040362497).

Then, after his speech, the President walked slowly down a ramp.  He appears to have some weakness or limitation in his right leg. His left leg does most of the work.  His pace slows down as he proceeds, until the last ten feet when he moves more quickly onto level ground.  Even on level ground, you can see that he favors his right leg. (See https://www.youtube.com/watch?v=FTvuVxUmnZ4)

Does the President have a problem with his right side?  Is there a neurological issue affecting him that the White House hasn't disclosed?  At his age (74), such a problem wouldn't be unusual.  But these problems can become serious over time and could affect a person in various ways.  Do we know everything about the President's health?