Do you have to complete a Master's degree before a PhD?

Many PhD programs will let you enroll with a bachelors. However, you are not skipping over the masters. You will spend the first 2-3 years of that program taking the masters courses, often doing a qualifying exam and/or masters thesis, and usually earning the masters degree before proceeding to the PhD work. So no, you don't need to have a masters in hand when applying to most PhD programs, but you don't get to skip it.

It is possible to get direct admission to a PhD program but you are not really saving yourself any more than 1 year of extra studies (and in practice even then you will be registered as an MPhil student for a year or two and then be formally accepted as a PhD candidate). It will depend on how strong your academic (not work!) references are and whether the university has any funding left for what you want to do research on. Remember that a Masters generally has fees that most people will be able to afford without a scholarship; this is not the case for a PhD. It is also possible in the US but you would have to be an exceptionally good undergraduate to be allowed to go straight in for a PhD.

The tricky part is, sometimes students from the same university are also applying for a PhD there after they just finished their Masters and they may have an easier time getting a place before your application is even considered; although if you had a Masters you would be given equal consideration, someone with a Masters will generally be viewed more favourably than someone with just a Bachelor's degree when going for PhD admission.

The cost of a Masters is relatively low and it only lasts about 13 months in the UK, so unless you are absolutely sure where you want to go to get your PhD you should do a Masters first so that you are better prepared for research. A PhD in the UK is a little different than what you might expect; there are almost no classes and it's all research in many cases.

No, it is not necessary. To be in a master's program serves the purpose of getting you more acquainted with the field of study your career or future studies will demand from you. Take my case, for example. I've already obtained my bachelor's in Philosophy; however, I am not foolhearted and did not apply to get into a Ph. D program right off the bat. In other words, you must learn to crawl before you learn how to walk is all I'm trying to convey here. Now, at the near midpoint of my M.A. studies, if I wanted to I could apply to a Ph.D program and not have second thoughts about my apprehension of the material because the experience and preparation I've accumulated has been great. Nonetheless, I plan on seeing through this current venture I'm on with my sights definitely set on getting the Ph. D afterward. Therefore, it is all relative on whether you want to skip the M.A. or see it partially or completely through while striving for a Ph. D.

In the UK, a masters is not necessary - I don't have one, yet I have a PhD.

Getting all the way to teaching is a long road, and very difficult. Many never make it to a teaching position, and then getting a permanent position is very difficult and will eat up years of your life. Think through long and hard just how much you are willing to give up for this, and if you are willing to make the sacrifices.

Some Universities offer an Integrated MS+Phd ; further you easily get scholarships if you indicate in advance of your intentions for PhD (at least in the USA).

It depends on the university, but some will allow you to go straight to your PhD (but often, you have to have higher credentials grade-wise and an overall better application)

In almost all cases you will need a masters degree first./

Yes.