1) US. You must file a US tax return every year. The fact that you will owe no tax is not an exemption from filing. The $80,000 exclusion is only valid with a timely filed return. You could elect not to file, and just wait until you "have" to, but then you run the (very small) risk that the IRS may reject your $80,000 tax free exclusion on the grounds that it was filed after the due date. While I have never seen them actually do this on a late filed return, they do have the right to do this.
2) Sweden. Once you leave Sweden, you only have to file Swedish tax returns on rental income from Sweden. You may also have to pay tax on the sale of Swedish real estate that occurs after you leave. If you salary is from Sweden, there are tax breaks that would allow you to tax it in either UK or Sweden, depending on the particular circumstances of your case. All your other Swedish and UK income would be tax-exempt in Sweden.
3) UK. You file an annual UK tax return in the UK if you have any income or expenses not covered by your withholding. The UK withholding is very accurate, and you shouldn't need to file if you are on a UK payroll having UK tax withheld and have no other sources of income.
Be wary of having investment income. The UK has a very creative system for avoiding tax on investment income. If you have a lot of investment income, you should seek professional guidance.