Concerning Icons, they are officially against them. They do honor the Cross (Much of the EO theology regarding icongraphy comes from St. Isaac The Syrian, who himself was a COE person who spoke at great length of the importance of the Cross in Christian worship)
Now concering sacraments it can be a little confusing. You see if you read the Margenetha ("The Pearl") an official medieval era exposition of their faith. There are actually two official lists given in that book. The first looks very odd, it has what you mentioned.
What I see is that they don't include "Anointing of the Sick" or "Matrimony" as sacraments, but they have three sacraments that seem to be similar or connected "Oblations, Absolution, Holy Leaven" and a completely different sacrament called "The Sign of the Cross."
The first list does seem to be the majority opinion (COE web sites list that one)
However when the Sacraments are mentioned again later in the Margenetha. The Second list is almost identical to the EO list (with marriage, annoting the sick etc.). It however seems like a minority opinion; because I'm not sure you will see that list pop up anywhere else.
However even in the original list there are some footnotes (I think added later by late PAtriarch Mar Shimun a few decades ago) and an oblique reference is made to using oil for healing the sick citing the book of James.
Also "back in the day" I brought up the weirdness of the list to a knowedgeable COE church friend. Especially the fact Marriage not being on the list but "The LEaven from heaven" was (Which looked very weird to me). The rationale for mariages ommision was basically a literal Biblical precenent. In Israel, brides were given away by their Fathers, and weddings were put on families they didnot take place in termples, synagogues etc. until much later (After Christianity seperated from Judaism). And the Assyrians have similar Semetic customs and ways of looking at things. Consequently they see marraige more as an instution of soceity, that has a church rite associated with it. And not as a proper sacrament. In that degree their out looks is fairly Protestant.