1) What term describes the phrase "in a way similar".
In the sentence in question, that string of words isn't a coherent phrase. That is to say, it's not an independent constituent. It's a preposition, a noun phrase, and the beginning of an adjective phrase.
The phrase "in a way" is, on its own, a prepositional phrase. The preposition is "in" and the preposition's object is "a way".
It remains a prepositional phrase even when the object involves additional modifiers. For example, "in a similar way" and "in a way similar to something else" are both still prepositional phrases. In fact, that second example is a prepositional phrase which contains an adjective which is modified by another prepositional phrase.
I've heard this property called chaining, but I think nesting is a better word for prepositional phrases inside prepositional phrases. Prepositional phrases can be nested to an arbitrary depth. I parse the original phrase as follows:
( in [ a way ] <-{ similar <-( to [ its use ] <-( in [ the description ] <-( of [ scheduled events ] ) ) ) } )
The innermost prepositional phrase is "of scheduled events", which modifies "the description". "In the description of scheduled events" modifies "its use". The phrase that starts with "to its use" modifies the adjective "similar". The adjective phrase starting with "similar" modifies "a way". Finally, the entire, huge prepositional phrase modifies the verb "use" in the original sentence.
2) Can a prepositional phrase like "in a similar way" be replaced by the adverb "similarly"?
In this sentence, yes, it can. The prepositional phrase that starts with "to its use..." modifies the adjective "similar". The same prepositional phrase can modify "similarly". That modified adverb can, in turn, modify the verb of its clause. The result is a sentence with a slightly different structure and much the same meaning:
I understand that the authors use the Present Simple similarly to its use in description of scheduled events.
