To be perfectly frank, this sounds like some sort of new-agey claptrap to me, but from a purely physical standpoint we cananswer this question.
First, let's define our terms. Infinite means infinite, not some arbitrarily large but finite number. And for "universe", let's be pragmatic and say we mean the observable universe, that portion of the universe that we can ever reach or that can ever affect us in any way, including by us just being able to see it. And finally, let's replace "intelligence", which is a pretty nebulous term, with "information", which we can define more precisely.
The most densely we can even imagine information being packed is one bit (yes/no, on/off, 1/0) per Planck volume... in practice, we are nowhere near being able to store information at that density; Planck volumes are much, much smaller than the smallest subatomic particles we know. There are a large but finite number of Planck volumes in the universe. So, there cannot be an infinite amount of information in the universe. In fact, the amount of information there can possibly be in the universe is pretty small as far as big numbers go; there are only about 8 x 10184 Planck volumes in the observable universe, a number so small that I could write it in full in a couple of minutes.
It is impossible to quantify the total intelligence in the universe as intelligence is a complex and varied concept that extends beyond human comprehension. The universe exhibits intelligence through natural phenomena and the intricate systems that govern it, but assigning a numerical value to its intelligence is not feasible.
It is not yet certain what size the Universe is, not even approximately - but it is probably not infinite. If you have seen an estimate about the number of galaxies in the Universe, it probably referred to the OBSERVABLE Universe, which is definitely not infinite.
The existence of matter is not infinite, as there is a limit to the amount of matter in the universe.
According to prevailing theories the universe has not existed for an infinite amount of time but is approximately fourteen billion years old.
Infinite intelligence is a theoretical concept; it has not been, and is not likely to be achieved by any person on Earth. In theory, infinite intelligence would allow the understanding of all things without limit. A being with infinite intelligence could figure out the solution to any problem.
Yes, there is believed to be an infinite number of galaxies in the universe.
Approximately Infinite Universe was created on 1973-01-08.
Yes, the universe itself is believed to be infinite in size, with no known boundaries or edges.
Those lists are both infinite. If you could specify a range, it would be easier.
A being of infinite intelligence may be considered "God" to some individuals. It is impossible to say what infinite intelligence could mean, or be represented by as a finite brain cannot fathom the infinite.
No. Matter is finite, and water is composed from two subsets of that matter. There is thus only a finite amount of water. However, because of cycles of use, it may be reused and if the required amount is low enough, the source can be considered infinite.
That depends on whether the Universe itself is infinite. It is not currently known whether this is the case.