What is the outcome of a human population starting with only 2 individuals?
Indeed natural selection decrease variability and therefore decrease information and mutation recreate this information. You can think of a bunch of pens of different colors. If you select 
for the red pens you will decrease the variability in pen colors as the other colors will slowly disappear. If you allow for mutation to occur you will recreate blue and black and purple and yellow pens to occur again in your population of pens.

Is it an accurate statement that less variability means less total information?

Yes, less variability means less information. Information is a concept that increases as predictability decreases. If no variability exist, you can predict at 100% what allele a given individual is carrying. You may want to have a look to shannon's theory of information here on Khan academy. Note: this has not much to do with biology but it has to the mathematical definition has to do with mathematics, probability and computer science.

Are there any known mechanisms besides mutation that replenish the variability in alleles?

No, there is nothing else than mutations that creates new alleles. "Mutation" means any kind of structural change of DNA. So by definition any change in the DNA is due to mutations, therefore only mutations creates new alleles. Note: that some people may use the word mutation in a more narrow sense including some kind of DNA change such as indels but excluding chromosome rearrangement for example. I used here the word mutation in the broad sense.

Segregation and Recombination

Two other concepts may interest you though: Segregation (See Mendelian inheritance) and recombination(also called crossing over).

For example if 2 individuals $AB$ (Allele $A$ on one chromosome and allele $B$ on the other chromosome) reproduce they can create the individuals $AA$, $AB$ or $BB$ thanks to segregation.

Two Genes set on chromosomes and if two genes are on the same chromosome, one might think that these two genes cannot segregate independently one from the other, they are linked! For example imagine an individual has the alleles $A_1$ and $B_1$ on two loci of one chromsome and alleles $A_2$ and $B_2$ on the two same loci but of the homologous chromosome. If this individual transmit the allele $A_2$ it must necessarily transmit the allele $B_2$ and can't transmit $B_1$ if recombination does not occur. But recombination does occur and allows for partially independent segregation of these two genes.

You will find more information about these two concepts on wikipedia. I don't want to go too much into details but in short these processes can in some conditions increase the phenotypic variance but in any case these phenomenon do not create new alleles. New alleles are created by mutations only.

Can 2 individuals carry as much genetic information than today's world population?

No! As a very simple argument, two individuals can only have 4 different alleles. But we know several loci (sing: locus, position on a chromosome) where there exist more than 4 different alleles. Therefore, mutations must have happened at some time.

And only to enjoy some further arguments: if these two individuals had together 4 alleles at all loci, it would be extraordinary unlikely that their variation would have remained in today's population. Let's imagine two heterozygote (=who has two different alleles on their two chromosomes for a given locus) individuals are $AB$ and $CD$ that have two offsprings. The probability that their 4 alleles are present in the two offsprings is $1/4$. I don't when Adam and Eve were supposed to exist but it very sound like their variability would have not been maintained through times. This random process which diminish variability is called genetic drift. To be a bit more accurate, in a population that do not change in size, the expected loss of alleles due to genetic drift at each generation $1/2N$, where $N$ is the population size. So the bigger is the population size, the lower is the loss of alleles due to genetic drift. In the above example $N=2$ and therefore the expected loss is $1/4$.

I don't know that much about meiosis, but isn't there a very limited number of alleles that could be passed on by the parents?

Yes, as said above, one individual can only have two alleles at a given loci and can therefore not transmit more than two different alleles.

Without a population to start with, wouldn't the lineage eventually turn into clones of each other[..]?

Yes, because in absence of mutations (and in absence of different special types of selection such as overdominance) the variability is slowly lost due to the randomness of segregation. This process is called genetic drift.