The problem with that mosque is that the people there claim that Sa'd bin Abi Waqaas radhiallahu anhu is buried there, when he isn't. The grave is even labelled in Arabic as قبر أبي وقاص (qabr Abi Waqaas or grave of Abi Waqaas). Problem is, in Arabic, "Sa'd bin Abi Waqaas" means "Sa'd, son of Abi Waqaas") so either this Abi Waqaas was the father of Sa'd bin Abi Waqaas rahdiallahu anhu (which is not possible) or some other person who was named Abi Waqaas (most probable explanation).
What you've mentioned is Islamic architecture, not Arab architecture. There were no domes or minarets in Arabia before Islam and if there were domes, they belonged to Christians and were probably an import from Europe.
As for symmetry, that is a result of Islamic architecture, since Islam forbids physical representations of living creatures (animals and human beings) so architects and artists had to make do with what they had, which was to work with geometrical shapes and come up with patterns. Even the Chinese mosques depicted would fall under Islamic architecture since there is a conscious effort to not incorporate animate beings, such as dragons and animals so often found in Chinese architecture.
Domes are probably the result of Arabs adopting it from the Byzantines and then bringing the idea to other Muslim countries. As for the minarets, they are a practical part of Islamic culture as the muaththin would climb atop them and call people to prayer.
One of the major reasons that many mosques go for the dome+minaret look is because they have become a distinctive symbol of Islam, especially in the West, where it is difficult to locate mosques.
And there was going to be a gigantic, very non-traditional, modern mosque that was going to be built in the UK near the Olympic stadium but petitioning by Islamophobes under the guise of "protecting the environment". Right now, the project is in limbo due to various controversies being linked to the mosque. Most of these claims are utter fabrications, such as the claim of terrorism link (surprise surprise!).
Read this utter nonsense to see the level of hatred against the group that is building the mosque.
Here's the website of the architect and the proposed design of the mosque:
http://www.myaa.eu/projects-detail/?id=1059&filter_by=region&value=europe
it is the caps that are hard to get. If you are in the states, Shukr does some nice stuff, but I had never (before Xinjiang) found a nice hard turban cap.
