1. Dear *****, your sister's husband can get a visa as the spouse of your sister and come and live and work in the UK. However, your sister will have to show she has earnings in excess of GBP 18,600 per annum in order that her husband can some and join her permanently in the UK. This will get him a visa as spouse of a UK national. The decision on this visa normally takes six weeks.
2. Here is a link to the UK government website which sets out the parameters of the visa he would apply for. https://www.gov.uk/remain-in-uk-family/overview. Under the heading of "apply" you will find an application form which he can fill out and make his visa application. The visa is for 2.5 years initially and he can get it extended for another 2.5 years at which time he can apply for settlement and Indefinite Leave to Remain. Citizenship can follow one year later.
3. Please Accept or Rate the Answer as unless you Rate the answer your Expert does not get paid for answering your question.
4. There is no need for her husband to go back to Hungary. If you look at the page i have indicated, it states it is people who wish to Remain in the UK. That means her husband can apply from within the UK. Secondly, the average of a year's earnings are taken. Your sister would normally need six months earnings to show. However, if she can show she has a good job and a contract she will be able to use her yearly earnings figure. Thirdly, I would not recommend using your sister's Hungarian passport. Essentially, the courts have held that when in Britain a British national must use their British status and nationality. Whilst there are fewer prerequisites for permanent residence of her husband if she were Hungarian, she is not allowed to use her Hungarian nationality when she has British nationality.