I didn't realise you were so liberal. What you've mentioned here are some terrible acts that everyone can agree need to be eliminated, but don't have a great deal to do with immigration. There are also British people who are vehemently homophobic, agree with the death sentence (there was a thread on this forum recently about it) , and then you mention cultural separatism. These points are sounding awfully familiar...
FGM again has some misleading statistics. I was using my good friend Google to help back up, something I really recommend doing when making sweeping statements (this goes to everyone here btw), I noticed sentences like "The BBC was among the news outlets to report this week that 137,000 women and girls in England and Wales may be victims of the practice." That doesn't say it's happening here. It's saying there are 137,000 victims living here, meaning it could have happened in a different country and they came here. British people mutilate each other too.
What groups are you referring to which have their own legal system? One I have quite a lot of experience with is the Charedi community, they have the Beth Din which in some ways is supported by British law. Because this community is so separatist and insular it works for them and they run their life by this law system. There are conflicts with British law sometimes, but there are more and more changes every time this happens and the courts will almost always favour British law. Anyway, most Charedi's living in Britain are British, not an immigrant population.
Everything you've mentioned here is applicable to both British and foreign born people and not an excuse to close our doors to people in need. You may not like cultures which aren't your own classic British, and that's fine, you have your culture, friends, food, areas you go to express your heritage and upbringing. Being the liberal you are though, it's surprising you'd want to see many people suffer and die around the world because they are different, and no one is forcing you to be like them. It's been mentioned many times earlier in this thread that immigrants give more to society than take away.
I would like to take a side here and that a lot of lines are getting blurred. Islam is not an immigrant population, it's a religion and therefore someone can be a British Muslim, so those insinuating we "send them back to where they came from" that's probably areas like Harrow in NW London, Finsbury Park etc.
On top of this, there are different immigrant groups and not all immigrants are the same.