I have got two offers to study for a Phd degree. I really hope I can finish it in 3 years. Recently, I have discussed about the prospect of doing a Phd in another Uni and I was told that I am expected to make publications and attending conferences. While it is a good idea to publish and attend conferences, do you think they will delay the completion of my thesis? Do all Phd degrees expect candidates to publish?

It is a good idea to publish and attend conferences if the money is available to do so. More than anything it will be a useful thing to have during your PhD viva at the end of your PhD which is a very important and decisive part. Having some publications on your work will act in your favour as testimonies of accepted works and will help you defend more strongly. Apart from this, if you want to pursue an academic career, the publication record will be very useful too.
I don't think writing papers will delay your submission because if you have written up for your paper, it will actually reduce the time of writing a chapter in your main thesis which will essentially be just about expanding the content of your paper. So, overall it is a good experience to be able to write papers, although it will mean that extra bit of work. :)