Change in genetic variance
From what I have been taught, Natural Selection (or even Artificial Selection) is great for panning favorable genes from a species and bringing them to the fore, however, it does not introduce new genetic changes.
Yes, you are pretty much right. In a given population, directional selection will ultimately reduce genetic variance (Natural Selection selects for a few variants letting the other variants disappear and therefore diminishing the genetic variance) while mutations bring variance back to the population on which further selection can occur.
To go slightly further (but without developing this part too much): Genetic drift decrease genetic variance (on average). Balancing selection (such as negative frequency-dependent selection or spatially heterogeneous selection for examples) help to retain variation (but never create more variation) in comparison to what genetic drift alone would do. Different kind of spatial population structure also affect patterns of genetic variation. The important point to understand is that in an isolated population, mutation is the only process that can create new variants.
Mutations in multicellular organisms - Somatic vs. Germaline mutations
You seem to call complex organism what we usually call multicellular organisms. You are very right that some mutations might be passed on while others won't.
As you said, a mutation occurring in the left leg will never be found in your gametes. We call such mutations that can't be passed on somatic mutations. On the other hand, mutations that can be passed on are called germline mutations. Of course, in unicellular individuals, all mutations are germline mutations.
[..] aren't those already rare mutations only passed onto offspring if they occur in the short-lived sperm or egg cells of one of the parents
Germline mutations are not only mutations that occur in the eggs or the spermatozoids (egg and spermatozoids are called gametes). Germline mutations are any mutation within the lineage of the gametes. For example, a mutation that occurs during mitosis during the morula phase on the right cell is also a germline mutation. A mutation that occurs in the testis during the division of a cell type Ad spermatogomium to give rise to another type Ad spermatogomium and a type Ap spermatogomium is also a germline mutation (see figure at the bottom of this answer and see the Age-specific mutation rate section). There are therefore tons of divisions during which germline mutations can occur in big multicellular organisms, while (germline) mutations can occur during only the single cellular division in unicellular organisms.
How many new mutations do humans passed on to their offsprings?
Generally speaking, the germline mutation rate per nucleotide is around $10^{-8} \text{or } 10^{-9}$ but don't consider this value too much as the per nucleotide mutation rate varies a lot between species and especially between different genomic regions. FYI, the haploid human genome (just to consider an example) consists of about 3 billion ($3\cdot 10^9$) base pairs.
The number of new mutations per offspring in humans is a Poisson distribution with mean and variance of about 100 mutations (this estimate might be quite inaccurate). This is maybe more mutations that you may have expected.
Age-specific mutation rate
There are typically a lot of cellular divisions happening in the testes in order to produce the very important number of spermatozoids a male produces in his lifetime (See figure at the bottom of this answer and see spermatogonium). Mutations also occur during those divisions and therefore we observe a correlation between the age of the father and the number of new mutations transmitted to the offspring. Hong et al. (2012) suggest using the following formula. The number of new mutations transmitted to the offspring by the father in humans is equal to $25 + 2(g-20)$, where $g$ is the age of the father. Of course, this is just a formula that matches quite well the observations but has no theoretical meaning. This formula applies only to males that are older than 20 years old.
Drake's rule
Empirical observations show that the higher is the number of base pairs $n$, the lower is the per-base-pair mutation rate $\mu$. This correlation between $n$ and $\mu$ is roughly linear with a slope of about 1. In other words, the genome-wide mutation rate $U = \mu \cdot n$ is more or less constant in all species. This correlation is referred to as Drake's rule and again, it is a rough approximation of a more complex reality.
Sexual reproduction vs Asexual reproduction
I am not exactly sure why you are talking about sexual reproduction in your post. Note that the mutation rate during meiosis (a process that occurs during sexual reproduction) is much higher than the mutation during mitosis.
Mutational effects
The mutation effect is the effect of a given new germline mutation. Of course, not all mutations have the same effect and there is, therefore, a distribution of mutational effects. Most recent studies (often mutation accumulation experiments) tend to show that a highly skewed gamma distribution (the negative exponential distribution is a special case of the gamma distribution) is a good fit to model the distribution of mutational effects of either beneficial or deleterious mutations. So the whole distribution of mutational effects is estimated to be best modeled by a gamma distribution for the beneficial mutations and a reversed gamma distribution for the deleterious mutations put side by side (where the density probability of having a perfectly neutral mutation is at the intersection of the two gamma distributions). The exact parameters for those distributions are likely to vary depending on the species but most likely depending on the exact stretch of DNA under consideration. Different papers offer different estimates (the work of P. Keightley on the subject is particularly influential). You might want to have a look at this answer for a summary of empirical data on mutational effects... The two gamma distributions need to be rescaled to make sure that the whole thing sums up to one and I don't know of any paper that suggest actual parameters for this rescaling.
Probability of fixation
Fixation is the event of a given allele (=variant of a gene) to reach a frequency of 1 in the population. In other, one allele is fixed, whenever at the locus (=genomic region of arbitrary size) under consideration is not polymorphic anymore in the population. The probability of fixation of a given mutation is a very important statistic. Let's call $s$ the mutation effect (if $s>0$, the mutation is beneficial). The probability of fixation of a neutral mutation given the population size is $P(s=0 | N) = \frac{1}{2N}$ (assuming a diplontic life-cycle) as it can be demonstrated from Coalescent theory, Wright-Fisher model of genetic drift or Moran (birth-death) model. The probability of fixation of a beneficial mutation is higher, while the probability of fixation of a deleterious mutation is lower. Those probabilities can be estimated with different techniques that use different assumptions: Haldane's technic (assuming that the number of offspring follows a Poisson distribution), Kimura's technic (using diffusion equations), Birth-death models, etc... Some methods assume small values of $s$, some others assume that $2Ns >> 1$, etc..
Number of new mutations in the population and rate of neutral substitution
If the genome-wide mutation rate for neutral mutations is $U_n$ and the population size is $N$, then there is a Poisson distribution of the number of new mutations at each generation with mean and variance $2 \cdot U_n \cdot N$ (assuming a diplontic life-cycle). Because each one of these mutations has a probability $\frac{1}{2N}$ to get fixed, the rate of neutral substitution in this population is $\frac{1}{2N}\cdot 2 U_n N = U_n$. Therefore, the rate of neutral substitution is a function of the genome-wide neutral mutation rate only. This classic result is used in estimating time since the last divergence between sister lineages (molecular clock)
Did you say Mutation Theory?
I have never heard of Mutation Theory. I am pretty sure Mutation Theory is NOT an existing concept (but the question is clear).
Spermatogonium figure
