Yes. It works for all adjectival Genitive endings and the form of он (его). Also for сегодня ("today"). Remember that Accusative also copies Genitive for some nouns, in which case the spelling also sill be the same as in Genitive.
Consider it a historical spelling.
Both sets are the genitive (and accusative) declensions of он, она, оно, and они. But whenever a preposition preceeds one of these pronouns and thus causes it to decline, н- is added to the beginning. You do not add the н if the pronoun is not preceeded by a preposition. Two examples: Я её боюсь (её is genitive because it is the object of the verb боюсь [бояться here=to be afraid of]) BUT Вот подарок от неё. (Она is again in the genitive, but it is genitive because it is the object of the preposition от, so it becomes неё). Hope that helps!
Г is usually pronounced as G in "gap" or "forgive". The Genitive -ого/его endings are an example of historical spelling that reflects older pronunciation for no apparent reason. The original sound, not unlike "h" in "aha" disappeared, then a V got inserted to separate the vowels.
Л is similar to "L" in "full". Except, in English you use this pronunciation after vowels, whereas in Russian it is the default pronunciation—which indeed may sound quite similar to V if the listening conditions are non optimal or you are unfamiliar with the sound. Try pronouncing "cold" with a "w" instead of an "l". Depending on how you do it it may sound awfully close to the original.
"Л" is never pronounced as "в" or "р", so it must be an audio glitch. Or it's the result of Russian "л" having slightly different sound from English "l"; some English speakers might hear it as other letters, because it sounds unfamiliar. In that case you just need to get used to it.
As for "mute" it doesn't happen often. "Л" is silent in the word "солнце" ("sun") and some of its derivatives, and that's pretty much it. At least I can't remember other such instances from the top of my head. So don't worry about it.
Ничего means "nothing". In Russian, when the sentence is negative all indefinite pronouns are automatically replaced by their negative counterparts: this includes all pronouns referring to "anyone", "anything", "in any way", "anywhere" etc. So, you use ничего, никто / никого, нигде, никуда, ни о чём, ни с кем, никак, никакой etc.
Note that «ничего» is Genitive, as would be expected with нет (нет кошки, нет стола, нет мамы, нет меня, нет никого, нет ничего). Moreover, it virtually never appears as the Nominative «ничто», at least not in the beginner's sentences. One example might be «Ничто не вечно» (Nothing is eternal, Nothing lasts forever), which, handy as it is as a wisdom, is hardly a structure you would use to make your own sentences..
Also you might see how simple prepositions split such negative pronouns:
- «О ком ты думаешь?»—«Да так... ни о ком».
Which roughly corresponds to "Who are you thinking about" "Never mind... About no one (in particular)".
You could express "Nothing is eternal" with Нечего вечного, right? I suppose that's more literally "There is nothing eternal," but that's essentially the same thing. Would Ничто...не be more common than нечего in this kind of construction (which is just basically Ничего нет anyway...)? I've never seen that, but then again, I haven't read that much yet and then when I do, I get really confused by Pushkin's там некогда гулял и я at the beginning of Евгений Онегин meaning "There I too ONCE/IN A FORMER TIME walked..." I know now that's an archaic/poetic meaning but that confused me for a while.
нéчего ≠ ничегó.
Мне нéчего есть — I have nothing to eat (1 negative part: нéчего)
У меня нет ничегó съедóбного — I have nothing edible (2 negative parts: нет and ничегó).
There are a lot of similar pairs: никудá-нéкуда ("where do you go — Nowhere" for the first word, "I have no place where I could go" for the second one), никтó-нéкто (nobody-somebody), ничтó-нéчто (nothing-something), etc. You don't need this information in the beginning of this course (the rule is pretty hard to understand, even native speakers learn it on 6-8th year of education), so just try to notice the original spelling.
Maybe a way to remember this is:
To imagine someone having an inexpected guest, looking in the fridge or cupboard, about to offer the guest something, but finding the shelving barren, makes the statement: "I have..no, nothing." Would be awkward, but because мышь едят всё!! this may have happened!