EP holder working overseas

Only a Singapore registered Company can apply for work pass (EP or DP). All foreign companies must have a registration number here before they can operate in Singapore.

If your EP is approved then you are considered as working in Singapore. So, your company is legally payable of your income tax on fixed salary and any other income associated with that job such as bonuses.

If you’re in overseas and unable to file return, then company should arrange.

Note: As long as your EP does exist, you suppose to pay the income tax here. If you only come here for attending seminars or meetings then your company better apply business visa in order to avoid paying taxes in Singapore.

You need a work visa in the country (or countries) where you actually work.
You will thus need one (and probably pay tax, depending on that country's rules, which I don't know) in the other country you mention.
From your description, it is not clear whether you also need a work visa for Singapore. Ask MoM!
You will then definitely have to pay tax in Singapore, too, at least for the work performed here. If your overseas work is seen as incidental to your employment here (e.g. business trips) you will have to pay tax on your entire income here.
Unless the other country has a tax treaty with Singapore that prevents it, double taxation is possible. Ask your company's tax or expartiation expert or engage an external tax consultant to figure this out in detail!