Learn English – What do you call the person whom you ship your product to

I'm afraid that there isn't a single word meaning our company as opposed to another company in English. If it's too confusing to use just plain company, then you may have to come up with some form of us, this company, our company, etc. on the one hand, and affiliate or associate companies (or client, if that's applicable) for the companies "our company" is working with.

It depends what kind of reference we're talking about.

Referrals, as suggested by @Autoresponder, is the normal term for "unsolicited" endorsements - for example, A is a satisfied customer who suggests to others that they should consider using B's products/services.

Reference (sometimes referee) is normally used in contexts where B suggest to someone that they should contact A for a "third-party" (in principle, unbiased) opinion on the quality of B's products/services.

There are many other types of recommendation, obviously. Proposing someone as the chairman of a group you're in, or as a suitable romantic attachment for your unmarried sister, for example. The list of words available for all the different contexts is too long for me to even attempt a summary.

I would say the process by which we create words such as recommendee, recommender, and recommendation from [re]commend is linguistic production. The prefix re-, and suffixes -ee, -er, and -ation are usually referred to as productive. Often contrasted to other prefixes/suffixes which were used to form new words in the past, but which are no longer considered acceptable for use in generating new word forms today.