Oh, yes. The 7 laws of Noah are, in my opinion, the basic laws that were used for non-Jews in the land of Israel, at least during a later time.
Orthodox Judaism and sometimes Conservative Judaism also understand them to be the laws for all non-Jews. No form of Judaism expects non-Jews to be Jews and the traditional explanation is that non-Jews are only required to follow these laws, which were given to Noah and followed by him and other righteous people who were not Jewish. And they are only judged by these. Some religions are considered as following the Noahide laws. The laws are:
Do not murder.
Do not steal.
Do not worship false gods.
Do not be sexually immoral.
Do not eat the limb of an animal before it is killed.
Do not curse God.
Set up courts and bring offenders to justice.
And I know this might seem a very strange question but as I've never been inside a synagogue, or indeed any other religious building bar the Christian ones.
Is there any form of iconic decoration, like the cross that hangs in a church inside the synagogue?
Well icons of any kind are avoided in Judaism, as far as worship goes, although that's not to say there won't be decorative symbols on the walls or even stained glass, none of this is really connected to worship and a synagogue could just as easily be a room with bare walls. There are a few things that would probably be present in a synagogue. One is the ner tamid, the eternal light, which is above the ark. This is a reminder of the eish tamid, the eternal fire which always burned inside the Beit HaMikdash.
There is also the ark itself which holds the Torah scroll/s. The scroll is made the old fashioned way by a scribe called a sofer.
There's also the tallit or prayer shawl which is only of value because of the fringes on the four corners and the tefillin and worn usually just in the morning or phylacteries which are the leather boxes containing parchment with scripture that are strapped to the arm and worn on the head on weekday mornings.
I can't think of anything else that looks different. Some Jews rock when they pray. There's some bowing. And services are all or mostly in Hebrew. None of the things I've mentioned above could really be considered icons though.
the tefillin were actually my first formal introduction to Judaism (the pursuit of studies) because of the parchments and the particular texts involved and this reference "you will wear the tefillin like a sign upon they hand and a memorial between thine eyes" and "remember your future" .... and I was also fascinated to learn that the hebrew words could be read the same from either side .... this made me think of the concept of "as above, so below" .... and lastly the creation of the word saddai from the letters shin, daleth, and yod ....the word saddai (which I understand to mean 'my breasts') related to a concept that god is both visible and invisible (completely unveiled he would be an idol; entirely veiled, he would be absent) .... I may not have a clear understanding of all the symbolism, but it is very powerful and I suspect until the day I die there will always be so much more to learn about this great tradition ... this study evokes great passion and that is an energy that is unstoppable .... he hawai'i au,poh