1) To qualify for foreign income and housing exemption exclusion, we need to have foreign earned income. It is more than we are in terms of residency. Therefore, you may need to consult with a CPA firm with international presence on the subject. For example, if most of your free lance consulting income is from the U.S., they are U.S. source income.
2) Since you can form company, it is probably best to have on your own tax return, wage income and dividend income. If you have the company, the company can report income tax to that country where it is formed and where it is operating the business and have income.
You can consider the social security and tax treaty agreement the U.S. signed with the various countries you are considering. Therefore, you can decide which country your company should issue your W-2 to you.
3) Unless we are very good at planning, the more countries you are involved with, the more countries' various taxes you may owe. We want them not to tax us, but they want to tax us.
That is, our residency, company and business operating locations, citizenship, source of income, etc. are all bases for us to be taxed by the country. The scope of taxes in each country's tax can be complex including not only income tax, property tax, sales tax. There are country and localities need us to pay consulting service sales tax.
U.S. is taxed with all income world wide. The location of its citizen does not matter. That is probably a recent trend is for citizens to abandon its citizenship. This is not what we are suggesting here.
Please feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP