The wikipedia page claims that likelihood and probability are distinct concepts. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a
The question is titled "Why is the likelihood function named as such when it does not appear to me to return likelihood?" to which the only possible answer is "the likelihood function does, in fact, return a likelihood." You acknowledge this answer in your post: "I am now understanding from Glen_b that the likelihood function does return ...
My guess: the quasi-likelihood is used to estimate model parameters when some aspect of the environment is unknown or unreliable, and restricted likelihood serves to add a regularization penalty?
2 To put simply, likelihood is "the likelihood of $\theta$ having generated $\mathcal {D}$ " and posterior is essentially "the likelihood of $\theta$ having generated $\mathcal {D}$ " further multiplied by the prior distribution of $\theta$. If the prior distribution is flat (or non-informative), likelihood is exactly the same as posterior.
Basically, likelihood of given model (defined by specific parameters and their values) is defined as probability of observing the data under the given model. In other words, we have some observed data and we then define likelihood function which takes model parameters as input and yields probability (or probability density in the case of countinous values of data) of observing our data if the ...
There's nothing about the definition of likelihood that makes it an inverse of conditional probability as a concept.
The likelihood function is a function of the unknown parameter $\theta$ (conditioned on the data). As such, it does typically not have area 1 (i.e. the integral over all possible values of $\theta$ is not 1) and is therefore by definition not a pdf.