Nenya or the Elessar?

[Galin]

So then if the Elessar was made in Gondolin, then it must be responsible for the growth of Mallorn in Gondolin, right? I'm not sure where i read it, but there was a mention of mallorns flourishing within Gondolin.

That's from a note in Unfinished Tales, but my answer would be: not necessarily (that they must be due to the Elessar).

Galadriel appears to do something quite notable, getting Mallorns to grow East of the Misty Mountains -- notable in that they would not grow in Lindon that is, a very western part of Middle-earth and a remnant of the Drowned Lands, so to speak; and peopled by Elves, including High Elves -- and the Mallorn (with soil) of the Shire also hails from her of course.

Was this aided by Nenya? again I'm not positive, and maybe I'm not giving Galadriel enough credit. Perhaps it is because Galadriel is her great self, but in any case Nenya could be employed in the Third Age, before Cerin Amroth was raised at least (according to a passage in Unfinished Tales), and so the idea came into my head.

But that is only one 'possible' scenario anyway, and if I have missed something that shows the Mallorns are (or must be) present in Lorien in the Second Age, then I must abandon the (specific) idea of Galadriel using Nenya to help the Mallorns take root, as she would be using her ring before Sauron lost the One.

One other thing, it seems that the Silmaril has this rejuvenating power as well. Was it really the Elessar at work in the havens of Sirion, or was it the Silmaril?

I'm not sure this was meant to be an internal variation (not that you necessarily meant that it was). If not we have two (external) arguably competing ideas, with the Silmaril noted in The Tale of Years for instance (The War of the Jewels):

511 '... reach Sirion, which now prospers in the power of the Silmaril' CJRT notes here: 'Cf. the Quenta (IV. 152): 'for them seemed that in that jewel lay the gift of bliss and healing that had come upon their houses and their ships; also AB 2 (V. 143).' And of course he chose the Silmaril for the 1977 Silmarillion.

I would have done the same