Do two: one using cash purchase and the other using a bank loan with 20% down.

Find a good REALTOR.

Should I BRRRR a property or pay cash for a couple mobile homes?

More importantly, though, I think it comes from being willing to push back and put in the work to find solutions to investment problems, rather than just accepting an answer at face value.

If the property has continued to appreciate, perhaps him buying you out at market value makes the most sense, then take the cash and roll into a new property.It sounds like you would like him to pick up another $500/month (pay you the $1,000/mo rent + pay 50% of the remaining mortgage split). 

Cash out my investment account and pay the capital gains2.

Smaller cities in the surrounding areas of Madrid, like Torrejon, Guadalajara, San sebastian de los reyes... etc always present some cash flowing option.

How do you find the neighborhood rating?

As another mentioned about finding a better rate with the previous owners company, gone are the days of just automatically renewing insurance and a good syndicator should be shopping around for the best coverage/premium atleast twice a year.

We usually bill our owner's via cash rather than accrual (IE our July owners statement for an owner has their July revenue minus expenses paid in July) but the owners get confused when the cleans don't line up to the stays, so had to train our bookkeeper to include the July cleans on the July statement even though that invoice was paid in August, which is different than how all the non-cleaner invoices are handled.