Re: brexit cost
1. Will UK actually save any money from exiting
Doesn't need to save anything, just needs to break even. The UK is a net contributor to the EU, to the sum of around £8.5bn per year (£160m per week, not the silly £350m gross figure that's sometime bandied about) so there is budget to cover extra costs.
2. Does government and general public has a complete understanding how to practically make this separation happen
Nope. Never been done before, no-one knows how it will come out. That's why there are two years of negotiations before the full details will be agreed.
3. I understand that biggest benefits are seen in restricting immigration
That is incorrect. Some politicians have been using that as an excuse, and some of the pro-remain campaign use it to claim that all leavers are racists, but it's not the major issue. It will have some impact: reduction in "benefit tourism", and the UK won't be subject to EU quotas for non-EU immigration, but the UK is already one of the most welcoming EU countries for immigrants (just behind Germany) by choice. That is unlikely to change significantly.
I think UK, and western Europe in general, has too generous benefits for people who are not working ... I would suggest to make much harder to such benefits, provide them for shorter time and immigration problem will resolve itself.
This control of "benefit tourism" is exactly what the UK government has been pressing for for many years, but the EU consistently refuses to accept it. It was a key part of Cameron's "renegotiation" platform, and the fact that the EU rejected it was one of the many reasons that people voted to leave.
The main reasons for leaving are economic. When the EEC was an economic group of co-operating neighbours it worked pretty well. When the politicians started to turn it into a trans-european empire it all started to go downhill. Economic stagnation, austerity as a failed cure, rising populism, refusal of the 'elite' leaders to listen, all signs of a group that is about to implode.
It's not surprising, every time someone has tried to unite Europe under one leader, from Cæsar to Napoleon, and on to more recent events, it's always failed and often violently. Never seems to stop them trying.
Being outside it will give the UK the opportunity to deal with other world countries on a level footing, not limited by EU policies and dogma. It won't be easy, but it will be better than going down with the sinking ship. It is a pity that it became necessary, though.