Hi Firewns,
Let me try and answer some of your questions based on my understanding.
Does this mean that anyone who has read and accepted conceptually the Ariya meanings of anicca, dukkha and anatta as outlined in this website will be assured of attaining the Sotapanna stage in the immediate future, as he or she would be a Sotapanna Anugami?
Short answer, no. Just because one reads, hears or accepts the dhamma he would not become an ariya. There is a level of understanding that is required. So one has to read and then understand it to be “assured” of attaining an ariya stage. There were lots of people (even monks) who heard the dhamma directly from the Buddha but did not understand it and therefore did not attain an ariya stage. However, without reading, hearing or accepting there is no way of being an ariya.
Would this same person lose his or her progress if he or she were to be reborn in a place where the Dhamma has never been heard? What if he or she was reborn in an immoral family? Could he or she start to veer off course?
Short answer, no. A sotapanna person is bound to attain nibbana and there is no hetu for him to veer off course. Since a sotapanna has no vicikicca, he knows the exact path to liberation and hence will not follow any other path.
However the Buddha only mentioned this after being asked this by ven. Ananda or Sariputta (I can’t remember who specifically). The Buddha later said that he hadn’t mentioned this earlier as people would become complacent and not strive to attain nibbana if they knew that they were an ariya.
Does a sotapanna understand these three characteristics all at once, or only one after the other at the magga moment?
Waharaka Thero mentions that if one understands one of these aspects, he will understand the other two at the same time. So at the pala moment all three would be understood.
Are any of the characteristics more easily comprehended than the others?
Yes. Based on the different gati and the development of each person’s indriya, they will be able to comprehend one aspect easier than the other. A person with a developed viriya indriya will be able to comprehend anicca, shadda will comprehend dukka and pragna will comprehend anatta easier. However this is just a general idea. It may differ from person to person.
Is it necessary to contemplate on pattica samuppada as well to become a Sotapanna?
It said that an ariya will have an understanding of paticca samuppada. So I feel that understanding PS is a result of comprehending the thilakkana. The different types of contemplations are given as aniccanupassana, dukkanupassana etc.