People get these nice Israeli silver gifts like kiddush cups or fountains -- do they need to be dunked in the mikva?
New [and certainly used] utensil's made of metal or glass require טבילה (ritual immersion) when one acquires them from a non-Jew (Orach Chaim, Yoreh Deah 120:1). Furthermore even if they had previously been acquired by a Jew, who in-turn sold/rented/gave them to another Jew, the dishes require immersion by the second Jew if this was not already done by the Jew who acquired it first (ibid 8). If a Jew made a utensil, sold it to a non-Jew, and then purchased it back from him then it requires immersion (ibid 11). The Shach 120:25 cites the Prisha in the name of the Maharashal that if one pawned his utensil and did not intend on redeeming it when he initially did so then immersion is required (even though this is generally not required for a pawned utensil even if one decided against redeeming it but then did).
If one buys a utensil in Israel were there is reason to believe it was made there but one is not certain, one should immerse the utensil without a ברכה [blessing](Igros Moshe O.C. 3:4). If one buys a utensil which indicates it it is from a country such as China where there is little or no Jewish community then it requires immersion with a blessing (ibid) unless one knows that the Jewish seller has already done so. As I understand it the Igros Moshe in question might not require immersion at all if it was made in an Israeli factory even if there are non-Jewish employees since they are paid by wage and do not in anyway acquire the material the utensil is being made out of and machines do the actual production [This is my half loshon kodesh-illiterate understanding of what he wrote, please feel free to correct me]. At any rate one could easily imagine other poskim having a different take about the status of non-Jewish factory workers so one should certainly ask a Rav l'maaseh.
This is my best read of the topic at the moment, but as I've already indicated I'm not great reading in loshon hakodesh and this is a topic I haven't learned inside before so be particularly mindful of the warning to consult one's Rav before acting l'maaseh.
Not if they were made and owned by Jews.
I'd asked HaZorfim a few years ago; if you buy it straight from them (or through a Jewish retailer), all of their stuff is made by them and they're Jewish, so no toveling is necessary. The exception is their Challah knives, which have an Israeli silver handle, but a stainless steel blade made in England (presumably by non-Jews).