Oh, aliens are very real.

Regarding point 1:
Drake equation only explores possibility in our own milky way. However, There are 125 billion galaxies in the observable universe only. So it is likely to be a lot bigger number, considering that the observable universe is likely only a fraction of the entire universe.

There is again roughly 100 billion stars in each galaxy. Each stars hold (at least) 1.6 planets, and then their are a lot rogue planets that isn't in a solar system (life can still emerge under ice, via thermal vents etc.).
We know, for a fact, that the chance of intelligent life emerging is not zero, because we exist. Considering how big the universe is, its very likely that it is going to happen again, likely before we existed (considering the age of the universe).

Regarding point 2:
Fermi paradox is basically a paradox saying that :
'mathematically considering that it is very likely that aliens exist, where are they?'
Great filter theory is an explanation to the Fermi paradox saying that:
'maybe there's some sort of a wall that destroys intelligent life as they grow?'

So, basically, if we find out that the aliens exist, Fermi paradox is literally solved instantly. Great filter theory also goes to dump since the Fermi paradox is resolved.
Technology part I will get back to it.

Regarding point 3:

Intelligent life has pretty big signature in space. For example, we have been shooting radio waves that are unmistakably artificial into space for over 120 years now(they seep out). So rather than finding just a specific grain of sand, it is more like a grain of sand that has an ever expanding force field around it that points exactly to where it is.

Considering their technology level, this is likely really easy to detect.

Regarding point 4:

There's probably nothing they want of us. Everything we have is plentiful elsewhere, why would they bother? As you mentioned, This is again tied to technology. Based on what we witnessed, their capabilities are:
- Near instantaneous acceleration to hypersonic speeds from zero
- Instantaneous change of vector direction that doesn't seem to be tied to momentum
- Dividing into multiple beings
- Suddenly appearing out of nowhere
- Suddenly disappearing out of nowhere
- Flying with no visible exhaust, wings
- Hovering STILL(no movement) with no visible exhaust, or wings
These are some of its features. Basically, they do NOT adhere to fundamentals of physics as known to humans. This is a level of technology that we couldn't even imagine having.

Regarding point 5:

There are likely several different alien groups (based on different types of UAPs witnessed). So we can't tell for certain what they want exactly, so its basically a speculation.

What I'd like to think is that, the level we've achieved is so trivial that they honestly doesn't give a F. They see us as ants. Or some ape community in a jungle. Scientists or enthusiasts occasionally come visit to fulfill their curiosity but that's about it.

For example, did you know that a monkey community in Brazil that has entered the stone age, 3000 years ago? Yes, quite literally. Some are intrigued, but nobody actually cares. I feel like its the same for them.

Extra point:

Lets think about it.
If not aliens, what else could it be?

Extraordinary phenomenon often require extraordinary explanations, and this rules out UAP being human activity from the list(no way anyone can hide this level of technology), along with mundane natural phenomenons such as ice crystals(because if it was natural, it would follow rules of physics and we would know).
If anything known is ruled out, we can only resort to explanations that involves unknown territory. And since we know a little bit about our universe; what we don't know is a very fragile territory. Its basically a speculation at this point.
speculation as in, its dictionary definition:
[noun] the forming of a theory or conjecture without firm evidence.
But anyways, Lets explore them:
- Would they be inter-dimensional beings?
- Would they be from different versions of our universe, per multiple universes theory?
- Would they be probes of the observers, per simulated universe theory?
- Or... Maybe, Would they just be aliens?
Since we can't prove the very existence of other dimensions or multiple universes, wouldn't it be most likely that they are aliens, from the very universe that we actually know really exist and measure, instead of some random one we don't even know they exist?

I don't know - you don't know - we don't know.
Its a speculation.

But honestly i do feel like the alien is the most likely explanation.