Does spacetime have friction? Yes, I'm thinking about the 'rubber sheet' example, but in 3 dimensions.  A typical animation observes the earth from slightly above the plane of the ecliptic, and the earth needs to "come up' out of it's own gravity well in order to move forward. But, if I place myself directly between the earth and the sun, head and feet on the plane of the ecliptic, the 'rubber sheet' makes it appear that the earth is falling into it's gravity well.  Now, I rotate 180 degrees, and the 'rubber sheet' makes it look like the earth is rising vertically out of it's gravity well.  The two effects imply that they cancel each other out.  Thus there is no friction in spacetime.
From another point of view, the event horizon of a black hole will not let light escape, let alone matter.  This implies that spacetime here, behaves like a (and I use for lack of a better term) 'solid,' which to me implies friction.
Then there is frame dragging (X stretching X).  Is this the effect of the black holes mass' friction on space/time? 
added 8/14/18:  
Further consideration leads me to believe that space/time does have friction, per SR.  When solved for mass; M=E/C2; SR tells us how much energy it takes to compress space/time.  At first glance, this might lead us to believe that Newtons 1st Law is false, and objects in space/time should slow as a result of friction.  Yet, for example on a sphere, for every place space/time has to be compressed for the sphere to move 'forward', there is an opposite point on the sphere where space/time exerts an equal force to decompress or regain it's natural shape.
 A: 
Yes, I'm thinking about the 'rubber sheet' example, but in 3 dimensions. A typical animation observes the earth from slightly above the plane of the ecliptic, and the earth needs to "come up' out of it's own gravity well in order to move forward. But, if I place myself directly between the earth and the sun, head and feet on the plane of the ecliptic, the 'rubber sheet' makes it appear that the earth is falling into it's gravity well. Now, I rotate 180 degrees, and the 'rubber sheet' makes it look like the earth is rising vertically out of it's gravity well. The two effects imply that they cancel each other out. Thus there is no friction in spacetime.

You are trying to get an idea of what 4 D spacetime is like, by comparing It to a 3 D world with pictures which are in 2 D.
Please let me make a small suggestion. Go out and buy a book (I can tell you what book it is, Relativity Demystified by David McMahon) and instead of using your imagination to get hold of an idea of 4 dimensional spacetime, use half an hour a day to read through this book and practise the math examples that are in it. 
You will gradually find it easier to think in proper equation terms and reduce the habit of trying to imagine anything that you can connect with the 3 D world we live in. To be blunt, try the math first and stick with it and forget the mental pictures, the math ones are easier in time and they are true. 
So I am not going to say a word about  friction and rubber sheet analogies. 

Then there is frame stretching. Is this the effect of the black holes mass' friction on spacetime?

You should be talking about frame dragging, not stretching.
Wikipedia Frame Dragging

Frame-dragging is an effect on spacetime, predicted by Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static, rotating for instance.
  This can and does happen around the earth, you don't need a black hole to check it.
The frame of reference in which a clock ticks the fastest is one which is revolving around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move past the massive object faster than light moving against the rotation, as seen by a distant observer. 

Ok, if you read that slowly it speaks for itself, eventually.  It means to get a distortion of spacetime, you don't need a big heavy black hole, a little light planet like Earth can produce GR effects just by rotating.

From another point of view, the event horizon of a black hole will not let light escape, let alone matter. This implies that spacetime here, behaves like a (and I use for lack of a better term) 'solid,' which to me implies friction.

No, you are going down a rabbit hole here. It's just as easy to imagine an invisible forcefield that only lets things in, because in effect that is exactly what it is. You don't have to think of solid walls or anything else like friction associated with them. This stuff is complicated enough with adding to your headache with ideas you don't need.
It's an invisible one way forcefield. That's the best image to use.
This is a short answer to your question about friction and you might have noticed there is something missing.
No Pictures.........you are better off without them because we cannot draw a 4 D spacetime in a 3 D world on a 2 D computer screen. I think when you say it like that, you might agree with me that is is stupid to even try, so I am not going to, in the hope that you buy the book and forget the pictures. 
A: This question is very interesting and actually the provided answer is not sufficient as it is based on the action principles and these are invalid when friction is present:
Frame-dragging is an effect on spacetime, predicted by Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static, rotating for instance.
The keyword is 'stationary'.
 This implies two statements: Obedience to the Principle of Stationary (Least) Action and equivalenty the conservation of energy.
So the sun-earth situation is frictionless in the theory, because it is assumed that this setup obeys to the principle of least action.
In case of a black hole energy is conserved by Hawking radiation. i do not know if a black hole violates the Principle of Least Action (time flow ?) but the situation appears a bit fishy to me and there is the known information paradoxon.
