1. Does the knowledge of regular sound changes help with learning a foreign language related to a language you already know?
It can help, but it depends on how you use the knowledge and whether you're the kind of person that learns best through making logical inferences. I learned Dutch, a language closely related to English, while outside the countries where Dutch is spoken, in part by teaching myself some basic linguistics. Within 6 months of coming to Amsterdam, I have achieved the highest level of language certification offered by the Dutch government.
However, when I tried to explain some of my technique to other learners in the Dutch class I took after I got here, I mostly got blank stares and/or looks of admiration without real comprehension, leading me to believe that this approach isn't for everyone.
Also, I found it most useful in developing an intuition once I already had a basic grasp of the language. I can't imagine it helping very much for learning the basics.
2. Does knowing an archaic language from some family help with learning modern languages from that family?
I would echo Pete's comment that knowing a related modern language is easier. This is the case for a couple of reasons.
First, languages within an area are not totally isolated, they will influence each other and often share innovations that were established after their divergence. For example, consider that most languages in Western Europe today use simple case systems with articles and word order used to convey ancillary information about nouns, despite the fact that both Latin and Proto-Germanic had complex and meaningful case systems with no articles and flexible word order.
There are not very many cases of a language being totally isolated from its relatives, simply because the technology for large numbers of people to travel large distances did not exist until relatively recently. One unusual example would be Finnish and Hungarian, which are members of the Uralic language family that are divided by many countries which speak Indo-European languages. Finnish has been much more influenced by Germanic languages than by languages that it is related to over the past millennium or so, primarily due to its history of Swedish occupation. That said, I do not speak either Finnish or Hungarian, so I could not tell you how similar they actually are.
The point is that nearly all languages have been influenced by their relatives after divergence, and so their last common ancestor is likely to be less similar to them than modern neighbouring languages.
Even without grammatical innovations, there are words in modern languages which simply did not exist in their ancient counterparts. For example, Classical Latin had no word for "tomato", because the tomato was not brought to Europe until the 16th century. It also would have had no word for "television", because the television was not invented until the 20th century. The things that we need our language to refer to have changed over time, and all modern languages have adapted, but ancient languages are suited to the era in which they were spoken.
On top of all of that, it is simply easier to learn modern languages because a) they have more native speakers to learn from, b) there are more resources available to learn from, and c) there is a broader and more active corpus of media in those languages. It would be far easier to learn and compare French and Spanish to each other than to learn Latin and then either one of them.
Now, if you are interested (as I am) in ancient languages as an intellectual curiosity and a source of ancient literature, then by all means study them, but there are far better options out there if your goal is to effectively understand modern languages.