Identifying parts of a sentence

Philadelphia...was a true eighteenth-century metropolis, the largest, wealthiest city in British America, and the most beautiful.

The phrase the largest, wealthiest city in British America is a noun group (a noun plus modifiers), and it functions as an apposition to the noun group a true eighteenth-century metropolis (it indirectly modifies it, as a kind of afterthought; it gives an additional description).

The phrase and the most beautiful is best considered elliptical: it stands for a longer phrase of which some parts are omitted. The longer phrase would be as follows:

Philadelphia...was a true eighteenth-century metropolis, the largest, wealthiest city in British America, and the most beautiful [city in British America].

So it is the short form of a longer phrase that functions as a second apposition to a true eighteenth-century metropolis.

Distilleries and breweries were thriving. Adams found the local beer so much to his liking that he temporarily abandoned his usual hard cider.

The verb find can be used with three complements: a subject (Adams), a direct object (the local beer), and an object complement (so much to his liking that he temporarily abandoned his usual hard cider). There are quite a few verbs that can have object complements, e.g. she painted the house green, I thought him quaint, I made the box larger. Object complements are somewhat similar to subject complements, in that they usually ascribe a property to or identity with the object: I found him stupid is similar to I found that he was stupid.

The subordinate clause that... is dependent on / modifies the pronominal adverb so: the word so expresses that it was to his liking to a certain degree (adverbial function), and it signals that the degree should be or will soon be known to the reader (pronominal function). When I say the wall was so tall, I might be using my hand to indicate how tall. So the word so refers to the degree or manner indicated by my hand. In your case, the degree is made clear in the subordinate clause that. It is very common to connect so with a that clause like this.