You might want to look into the Taxes section of the forum where you might find more info on the questions you have.
I know nothing about UK taxes, so I can’t help you on that side of things. However, there are usually ways to take a credit or deduction on foreign taxes paid even in the absence of a double taxation treaty or agreement.
In regards to whether you are treated as a resident or nonresident for tax purposes, it is based on presence in the ROC for any reason. If I read correctly, you were here less than 183 days last year, so you are considered a non-resident for tax purposes. The visa you are on or the reason you are in the ROC has no bearing, only your presence.
As for foreign income, ROC taxes are due on any income paid here. Income for services (‘earned income’) performed here but paid abroad is taxable if you were present for more than 90 days in the tax year. Investment income such as dividend distributions you earned abroad are not taxed. If you spent significant time out of the country after Sep 2, then you may be under the 90 days limit and you don’t need to worry at all. If not, then you’ll be taxed at the 20% non-resident rate.
As a practical matter, if you are considered a resident for tax purposes here, the tax office will be very curious about any earned income paid abroad and will want to assume that such income is related to your presence here, in which case they will consider it taxable. You may be asked to prove that any such income is not related to your presence here. This is something to think about in future years. If you are considered a non-resident then they are less curious about this.
As far as your income here, your business here will need to pay taxes on income being made here. From your other posts I assume this is for your representative office which is owned by a company in the UK owned by you. In this case the representative office would pay business income taxes on ROC business income, then you could send distributions back to the UK office which could then make a dividend distribution to you which would not be subject to personal ROC income taxes. Depending on how the UK treats foreign income, it may be more advantageous to take your income here if such income is not taxable in the UK.
Since you arrived late in the year and the business wasn’t formed until November, my guess is they probably won’t scrutinize your 2005 personal tax return closely if you don’t claim your foreign paid income.