What do you accept as proof of being self-employed? Would a declaration of my residential address (proven by ID/signed declaration) suffice?

A signed declaration regarding your residential address would not be sufficient as proof of your place of business. The type of proof which would be acceptable as evidence of self-employment depends on the country concerned. In most countries, a person must be registered as self-employed with the national authorities (e.g. the tax authority) of the country concerned, so a copy of a certificate from the tax office (e.g. VAT ID allocation) would, for example, suffice.