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I am of the belief that anything (almost anything) can happen if enough time elapses. 

It's like with evolution: creationists will say, "Hang on, how did this creature 'zap' into a new creature?" Yet the short film I saw lately, and the books I read, show it was incremental.

Does the word "incremental" not also apply to the birth and development of the universe?

The latest little daydreaming session I've had is that even though gravity is a "weak" force or seems weak because we simply cannot measure it as effectively as we think we can. It seems to me that the gravity from every object may extend the entire distance of the universe.

It does do this.  It gets weaker farther from the source, but it's never zero.   For instance, if you were standing on a tower that doubled your distance from the Earth's core  from where you are now, you'd weigh 1/4 as much.  Three times, it's 1/9th.  Four times, 1/16th as much and so on.  A very precise knowledge of how gravity behaves is necessary to send spacecraft to distant planets, etc.  The term "zero gravity" for what astronauts experience is, to be polite, really misleading.  "Free fall" is much more accurate.  The Earth's gravity in low-Earth orbit (where you are moving sideways at 17,500 miles per hour)  is almost as strong as it is on the ground, but spacecraft and astronauts are falling through it, so they don't feel any weight.  Gravity then "merely" bends their path into a circle around the planet.

>>Thats why black holes can keep whole galaxies of stars tied up.<<

Most of a galaxy's mass (more than 99%) is in the stars, nebula and dark matter orbiting the core.  These are really orbiting  the center of mass of each other  more than the central supermassive black hole.  If you could remove the black hole at the center, the rest of the galaxy wouldn't notice much.  The black hole is super-important for the formation of stars in the first place, but they tend to clean out the areas near them after a while.  If they become active later in their life (stuff falling into them), they can do stuff like this "Death Star" galaxy and shoot out a beam that blasts the crap out of neighboring galaxies.  

>>So that would also mean that Earth's gravity, as infinitesimally small as it is when compared to the entire universe, still has an effect on every object in the universe. <<

Eventually, yup!  It does, and of course vice-versa.  Note the effect is "communicated" at the speed of light, so that's why I said "eventually." 

Aside:  they just discovered a "ghost" galaxy with a cool name, "Dragonfly 44,"  that is 99.99% Dark Matter.  Nobody is going have a sci-fi story with that in it ever.  Nope.

But that energy comes from stars. We can send capsules with information in them, and we can broadcast on radio wavelengths. But these are minuscule efforts compared to the size of the universe - heck, just to the size of the Milky Way. How far could a craft have traveled since a launch in the 70s? I doubt it's traveled far enough to reach Centauri yet. And I'm not a physics expert, but don't broadcast signals degrade over time? Even if they don't, they couldn't have traveled farther than 40 or 50 light years by now - not very far at all.

We could conceive of a way to broadcast visual signals (e.g., making the sun a gigantic signal lantern), but we can't practically do it. It might be the case with other intelligences. Maybe they're sending us messages and we just haven't received them yet... and never will.

Of course, this is no proof either way of ETI - but it is a consideration. Until someone shows that FTL travel is possible, we may just have to resign ourselves to the fact that we're alone for the time being. A LONG time being.