Usage of "please" at the beginning of a sentence

Please report more details.
Please do not send your faxes from the office.
Please do not hesitate to contact us from our website.

Does please have the same meaning, in those sentences?
In the second sentence, could it be understood as I demand/ask you don't send your faxes from the office? What is the difference between please do not sent your faxes from the office, and do not sent your faxes from the office?

Please is probably a shortened form of the archaic "if it pleases you [to do this, ]". It is used to indicate that what follows is a request. It is considered polite. It suggests the other party has taken into account the feelings of the recipient.

Obviously, in spoken English, tone of voice, facial expression and body language can completely change the emotional effect of whatever words are spoken. In written English you have to be more careful.

An awful lot depends on context, you can read too much into the presence or absence of words like please.

In the examples you quote, it is likely the second would be used in two circumstances:

• when you have just sent a personal fax from your place of work - chastisement.
• when you are being introduced to working practises at a new job - it's not personal.

The other two are asking you to do something positive, the "do not hesitate to" really means "do".

You could argue that "please" has the same underlying meaning, but the pragmatics of how that meaning is interpreted can vary from context to context.

In the first two cases, the implication is effectively a command. The implication is not "You may optionally decide not to send faxes, and that would please us". It's a bit like an airport announcement saying "Passengers are invited to proceed to gate 4", which is not quite the same as if I "invite" you to a party-- they're not actually offering you a real choice to decline that invitation.

Many languages have this kind of pragmatic subtlty: if a Spanish sign says "Favor de no fumar", they're not actually implying "You would be doing us a favour if you decided not to smoke". If a French sign says "Merci de ne pas fumer", they're not actually saying "If you decide not to smoke, we'll be thankful".

In English, modals are another common area of this kind of subtly. If your boss says to you: "You might want to get this done by lunchtime", they're not making a supposition about your volition to do the task-- what they're effectively saying is "Do this by lunchtime"; I've heard cases of foreign employees getting caught out by this kind of device.