The former answer is from the perspective of Islam, which is only one perspective. In light of this, there will be many perspectives. Here is a Christian perspective.
God speaks preeminently in his Word, that is, the Bible. This is why Christianity is a religion of the book, just like Judaism and Islam. The author of Hebrews makes this point as God has finally spoken through his Son, who is the word of God.
With this said, many Christians would say that God still speaks through the Holy Spirit or even through our consciences. However, to say this is not to add anything to the Bible, but to use what is in the Bible in specific and incisive ways. Finally, others believe in more "miraculous" ways in which God speaks, such as dreams and visions.
The question is about the relationship of the people and God, and if we realise that there is a relationship then we believe in God.
Now coming to the first part: "Has God stopped speaking to his people?" I would say have we listened to what He spoke to us through His prophets in a large number of books? The prophets were sent for the Guidance of the people as He said:
Surely thou art a warner and every people have (had) a guide. (Quran Al-Raad 17:7)
But people did not listen so He sent the last prophet Mohammad and the Last Book where in He says:
This day I have perfected for you your faith, and completed My blessing upon you, and have accepted for you Al-Islam as religion. (Quran Al-Maidah 5:3)
It is imperative for the people to listen to Him and not think that He has stopped speaking to us anymore. Even now he is talking to us through Quran but we are not listening.
Now coming to the second part: "Is God speaking through the written word?" Well, the answer is yes and no. His words where passes on to the prophets to the messenger-spirits which were written by the people to preserve it, but it was not the case for all the books. In all the cases except the last one, original books were lost and the books were compiled later by the followers giving rise to different versions of the books. The written words have an advantage - these can not be altered unless the original are destroyed/lost and you compile new ones. Naturally the new ones are prone to changes due to many many reasons that I would not like to count. These books were for a specific tribe, nation or time therefore preserving those was not important for all times to come. However, when the last book was given for the guidance of mankind, it was meant to stay for ever in its original form. Hence God made sure that it was preserved by saying:
We Ourselves surely send down the Reminder and We most surely are its Guardians. (Quran Al-Hijer 15:10)
God is speaking to us even today through Quran but we are not listening and doing whatever we like, against the will of God.
Most surely there is a reminder in that for one who has a heart or who lends ear whilst he is all eyes (lit. a witness). (Quran Qaf 50:37)
This is nothing but a reminder and a clear Quran. That he (Mohammad) may warn him who is alive ... (Quran Yasin 36:69-70)
And those who have been given the true knowledge see that what has been sent down to thee from the Lord - that is the truth. (Quran As-Saba 34:6)
Still we are in doubt whether God speaks to us or not.