We will acquire a second-hand ultralight from its owner, which is a company. Is it enough with the invoice of sale, or does it have to make a contract, in addition, with a signature legitimised before Notary?

The Invoice is not a document inscribed either in the Register of Furniture Property of Madrid or in the RMAC. You can consult in the MOD 4 application, the type of document that must be submitted in both registers, through this link.