The Brachot (Blessings)
As mentioned above, the Chabad custom is to make the ha'etz blessing on the apple.
The custom in Sefardic communities is to make the bracha of ha'etz on a date (or a pomegranate if one does not have a date) since it is one of the seven species of Israel.
The Mishnah Berurah writes that one who wishes to make the bracha on the apple should remove the fruit that are from the species of the land of Israel from the table before doing so.
One need not make the beracha of ha'adama on cooked vegetables (e.g., pumpkin and leeks) as these are foods normally eaten during a meal and are “covered” by the HaMotzie blessing on the challa.
No Grapes
The Vilna Ga’on’s custom was to not eat grapes on the nights of Rosh Hashanah. Since the sin of eating from the Eitz HaDa’at took place on Rosh Hashanah and some say it was a grape vine, it is inappropriate to eat grapes at this time. Even according to this custom, one may eat raisins that are mixed into other foods.
Prayers on the Foods
According to the Shela (Rabbi Isaiah HaLevi Horowitz, 1565 - 1630), the main objective in eating these foods is that the person should be inspired when reciting these prayers.
Although eating these foods have significance, certainly doing Teshuva and increasing in mitzvot is more important.
If one does not like any of these foods, he may recite these prayers (or think them) while simply looking at the foods. In fact, the Talmud (Horayot, 12a) says that one should “see” these food items on Rosh Hashanah.
Chabad custom is not to recite these prayers with the exception of the yehi ratzon on the apple. (It would seem, though, that one should have these intentions “in mind.”) (It is noteworthy that, although most of these foods are mentioned in the Shulchan Aruch HaRav, it is not the widespread Chabad custom to be particular to have all of them.)
On the Second Night
Sefardim and some Ashkenazim have the custom to eat the above symbolic foods on the second night of Rosh Hashanah as well. The Chabad custom is to eat these foods on the first night only.
No Anger
The Mishna Berurah says that in addition to all of the above “signs” for a good year, it is obvious that one should refrain from getting angry during these days. Rather, one should be glad in his heart and trust in G-d together with (doing) teshuvah (repentance) and mitzvot.