Are mutations accumulating far faster than selected out?
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Is the rate at which new mutations occurring higher than the rate at which alleles fix today in humans?

Human populations are exploding! Genetic diversity within a population is a function of the effective size of its population. As the population expansion in human is extremely recent, we ought to expect that our genetic diversity is much lower than what would be expected from our population size and structure. Therefore, yes, genetic diversity is currently increasing, or in other words, more mutations appear than there are alleles that fixed.

Is the genome deteriorating?

I am not sure what you mean by "the genome is deteriorating" but the answer to "Is the genome deteriorating?" is likely no!

Actually, larger populations tend to suffer from less drift load and as such our mean fitness would rather be increasing. However, given the population size, I doubt that would make such an important difference.

On the other hand, medicine is greatly affecting our environment and is reducing the strength of purifying selection. As a consequence, modern populations would eventually be less fit than our ancestors if placed in the environment experienced by our ancestor (that is an environment with little to no medicine). But this will not be true in our current environment.

Prerequisite to understand the answer

This answer felt quite introductory but it actually contains all the following concepts:


Allele
Allele fixation
Genetic drift
Effective population size
Population structure
Drift load
Purifying selection
Genetic diversity (typically defined as the expected heterozygosity)
Effective population size
Environment (and even niche construction)


If any of the above concept is unclear to you (and I very much suspect that at least the term "drift load" will be new to you), then you might want to start with an intro course to evolutionary biology and population genetics.