Can one make kiddush and shechiyanu after plag hamincha on shavuos night, and daven marriv later after tzas hacochovim? Can a women light candles likewise after plag?
On Shavuos night a person should not make kiddush early, before plag ha-minchah.
This is ruled explicitly by the Magen Avraham (494), and is likewise implied by the Shulchan Aruch Ha-Rav and by the Taz. The reason for this is that making kiddush has the same halachic status as davening maariv: both bring in Yom Tov early, and poskim write (see Shelah, Shavuos) that this should not be done on Shavuos, in order to ensure that the “days [of sefiras ha-omer] are complete”.
See also Yecheveh Daas (6:30), who writes that one should certainly try to be particular for this opinion, in particular in Israel, where doing so is not difficult.
For lighting candles, there are variant opinions among poskim. Some write that candles should not be lit early, and this is the ruling giving by the Luach Eretz Yisrael.
However, based on the Shulchan Aruch Ha-Rav’s distinction between davening (and kiddush) and lighting candles (the former involving bringing in the the next day, and the latter being only tosefes Shabbos), some are lenient for lighting candles early, for those who have the general custom of doing so on Yom Tov. This is the ruling given in Halichos Shlomo (Yom Tov 12:2, see note 9).