Singapore IELTS & English tests - Study without IELTS

Can I get an IELTS waiver based on my bachelor's medium of instruction in UK/Singapore?

Is there a possibility of getting a waiver for English language tests (MOI waiver) for Singapore or other countries in Ireland?

Does studying in a state board affect eligibility for MOI waivers or admissions in Ireland/Singapore for a Master's?

Do I need to submit IELTS for my course in Singapore if I have an MOI certificate?

Are there other countries besides the UK that offer post-study work permits or stay-back options without IELTS in Germany/Singapore?