In addition to the elements you have identified, in "Rappaccini's Daughter," by Nathaniel Hawthorne, I notice not only that the house Giovanni lives in seems too solemn and crumbling, but the stone work that surrounds the fountain is falling away as well. It is broken, speaking of destruction or loss of vitality, but stands in stark contrast to the water that sparkles with life, nurturing the plants. Giovanni notes that the water seems like an immortal spirit, so perhaps the comparison is that the water looks alive despite the perception he gets in his dreams about the evil present in the garden, as an immortal being could not be touched by that evil.

Giovanni notes that the doctor must handle the plants with gloves and mask, perhaps symbolic of his separation from the living, reminding the reader that Giovanni was warned by Baglioni about Rappaccini's concern with the experiment more than people.

The doctor's obsessive behavior, as well as Beatrice's actions grab Giovanni's attention, perhaps alluding not to the bringing of life, but of madness—that will ultimately bring death.

Giovanni witnesses the death of the lizard by the poison of the flower. A lizard, according to St. Gregory "the Great," represents the "soul that humbly seeks enlightenment." (This is seemingly symbolic of what Giovanni is doing: so the lizard's death is a warning?)

This occurrence might well refer to Giovanni, but the lizard's death then takes on the semblance of foreshadowing as well as concern on Giovanni's part for the experiment.

The immediate withering of the bouquet Giovanni tosses to Beatrice also leads back to a warning in retrospect.

The hidden entrance that Lisabetta shows Giovanni might be symbolic of the threshold over which one passes between ignorance and knowledge, between safety and danger, from life into death, or light into darkness (good vs evil).

There is something symbolic, perhaps, in Beatrice's comment:

Believe nothing of me save what you can see with your own eyes.

This comment might be symbolic of a warning: she suggests that Giovanni's eyes should tell him the truth of what he sees. If this is the case, should not the death of the lizard, insect and the bouquet have been taken as warnings to Giovanni?

I hope that some of these ideas are of some help.

Recalling Nathaniel Hawthorne's being a Dark Romanticist, the character of Giovanni can be interpreted as symbolic of the human artist in conflict with science in the form of Dr. Rappaccini, the man consumed by his "exclusive zeal for science" who sacrifices the humanity of his daughter in its advancement.  

As in the Garden of Eden, Giovanni, like Adam, is tempted by the beautiful Beatrice, but he cannot touch her, just as Adam was forbidden to eat of the apple.  In his perception of Beatrice, Giovanni finds her both ""beautiful" and "inexpressibly terrible."  Giovanni, influenced by Baglioni, eventually comes to regard Beatrice as "poisonous thing" that has contaminated him. In his misguided attempts to save Beatrice from her evils, Giovanni displays his own selfishness by giving her an antidote provided by Baglioni that he hopes will "purify" her from evil.  As she dies, Beatrice asks Giovanni, 'Oh, was there not, from the first, more poison in thy nature than in mine?"  Like Adam, Giovanni has desired a woman to be his, but the results have involved sin.