Can I finance and buy easily in another EU country, or is it easier to do so in the one I have a passport for?...

References will become tantamount to a passport equivalent for those landlords who know what they are doing. 

Here is a list of documents I tend to ask for:Completed ApplicationPhoto ID (Passport or Driver's License or State ID)Most Recent Tax ReturnMost Recent W-2/1099 (If Independent Contractor)3 Most Recent Bank Statement (Showing Maximum Liquid Assets)3 Most Recent Paystubs-Student School Schedule and ID (if applicable)Pet License (if applicable)Pet Vaccinations Records (if applicable)Landlord Reference Letter (if applicable)Proof of Rent Payments (if applicable)CPA Letter (if applicable)If they can't provide sufficient documentation for you to approve them as tenants, then it would be better for you to move on to the next applicant.

Additionally, you should always request a copy of residents state-issued government ID, driver’s license or passport and a headshot and selfie.

She sent her passport and application for a visa to the Cameroonian embassy in DC. 

You know when it's being audited because the lender will ask for a social security of the buyer or even passport or drivers license, which typically NEVER gets asked for. 

Here's what I've got:- Copy of SS card and 1 alt. gov't issued ID (Driver's, passport, etc)- 4 weeks of paystubs, or most recent benefit letter showing $ of benefits- 4 weeks of bank statements for checking account- Last year's tax returnAm I asking too much from them? 

We verify legal status in the US by I-20 and passport.

Be more professional than using profile / FB type photos, a professional photographer isn't that expensive, they shoot passport types all the time, get a business like background, pose, they can shoot several times. 

Copy of Passport & Driving License4.