what is allowed to advertise in Facebook fan-pages?

Make your own page. Advertise whatever you want to, so long as it doesn't violate FB's Terms of Service (e. g. don't try to sell child porn, ferchrissakes).

Don't spam other people's fan pages. They can (and do) create their own expectations for use, and have every right to remove off-topic, illegal, and spammy posts.

Thanks very much, I suppose "your own page" means "your own Facebook fan-page" . What I am concerned is about a tiny FB statement on TOS which says something like "to make advertisements first ask for us", which is an impossible task (to talk with FB).

In this interesting page for instance they say that "affiliate links are not allowed through Facebook ads" , but I am confused if this applies to FB paid ads which have an affiliate link, or else to normal posts on FB page which contains affiliate links.

EDIT: MODERATOR: DO NOT POST LINKS HERE

The reason for me being to cautious, is because some times ago FB closed my personal profile (it forced me to change to fan-page) with a tiny msg "you are using your profile to make business", even when I never used it to make any kind of business, just to post links of newspapers focusing on tourism.

Yes, 'your own Facebook fan page' is what I meant. Not someone else's, not some company that you don't own. YOURS.

Facebook doesn't want you advertising using affiliate links, say, if you use a tracking code when people order a product through you, to some company that does not belong to you.

FB wants you to make FB ads. That is, they give a platform for creating ads for your business but they create the ad. It looks better and they can give you tracking metrics. Yes, they want to charge you (how, exactly, do you think FB makes money otherwise?). Can you use affiliate links that way? Possibly. Certainly you can advertise with a specific landing page for people to click on.

You are not allowed to put in your soap or sunglasses advertisement onto Facebook unless it is through FB, as a FB ad. Your linking, by the way, was probably flagged as these newspapers promoting tourism, I am sure, were not newspapers at all (the Boston Herald, for example, doesn't tout tourism except in a rather general sense, as does every other legitimate newspaper out there), but were a lot more likely to be ads made up to look like newspapers.

Here more a question about, suppose you have very popular fan-page and someone (maybe a seller) want you to share his post about a new product in your page, then you answer to him "ok deposit x dolars in my paypal and I will share you".

Is this allowed by Facebook?, ok FB actually is not able to know about these deals, but suppose someone tells to FB about, what would be FB reaction?

Again, there is nothing in FB TOS allowing (or not) these transactions.

No, this isn't allowed. It's a sale. I just got finished telling you - FB wants the commerce on their site to be through their ads.