The signature list on the Digital Signatures tab tells you the name of the signer. In the case of a company, this will typically be the name of the company, e.g., "Microsoft Corporation". If the two names are the same, the files were probably signed by the same company.
This isn't an iron-clad guarantee, mind you, because there are a large number of organizations that are trusted to sign certificates ("certificate authorities") and not all of them have entirely sound procedures for checking that the certificate they're signing really belongs to the person it claims to. But this is as good as it gets.
If you mean you're worried about distinguishing between two different companies with the same name (in different countries, perhaps) there isn't really any foolproof procedure. In some cases the two files might be signed with the same certificate. Look at the issuer, the serial number, and the thumbprint. If they're all the same, you can be reasonably confident that it's the same certificate. However, just because the certificates are different does not mean that they belong to two different companies.
Regarding your second question, the certificate file (".cer") does not allow you to sign a file, because it does not contain the private key.