The word as was formed long ago from two words. It is a contraction of all and so. But you must not think it means the same as our common word also. It means all so, entirely so, just so.

Sentence 5 means that John works in a certain way and that he plays just so. As is a conjunctive adverb. It joins the adverbial clause of manner to the verb works. As an adverb it is added to the verb plays in the clause and expresses manner.

In Sentence 6 the first as is a simple adverb of degree added to the adjective tall. The second as is a conjunctive adverb. It joins the adverbial clause of degree as her mother is tall to the first adverb as. As an adverb it is added to the adjective tall in the clause.