So, I think it's time for me to give you some insight, with a selection of articles and analyses I have found on the web.
Concerning the cohabitation between secularism and Islam in Turkey, I find this article most illuminating:
KONYA, Turkey: In the not too distant past here in Turkey's religious heartland, women would not appear in public unless they were modestly dressed; a single woman was not able to rent an apartment on her own, and the mayor proposed restoring a segregation of the city's buses by sex.
Fears of those kinds of restrictions have led thousands of Turks to march in many cities over the past month, inflamed by secularist politicians. A political party with a past in Islamic politics, led by Prime Minister Recep Tayyip Erdogan, has tried to capture the country's highest secular post. Once it succeeds, their argument goes, Turkey will be dragged back to an earlier era when Islam ran the state.
But here in Konya, a leafy city on the plains of central Turkey, the rule of Erdogan's party has done no such thing. In the paradox of modern Turkey, the party here has had a moderating influence, helping to open a guarded society and make it more flexible.
Full article (Source: Herald Tribune)
And what is going on between the government and the military? A "war of nerves" according to the Lebanese Daily Star, which explains:
(...) these tensions have heightened as a result of changes in the top echelons of the Turkish armed forces, particularly the replacement last August of General Hilmi Ozkok as chief of the Turkish General Staff. Ozkok was a moderate who maintained a low profile and sought to develop good working relations with Erdogan. By contrast, his successor, General Yasar Buyukanit, is a strong secularist who has been far more outspoken in asserting the military's views.
As for the constitutional reform, even the judiciary, whose independence from the power has been reasserted by the decision to invalidate the first presidential vote, does not consider it a threat:
Tülay Tuğcu, Chief Justice of the Turkish Supreme Court, said that parliament-approved changes to the constitution that would allow Turks to elect their president by popular vote do not mean a “regime change in Turkey.”
Full article (Source: Hürriyet)
But there is a category of people who see themselves threatened by one of the reforms: the Kurds, as explains in detail France Presse:
But why do secularists oppose the reform? The answer is in Southeast European Times:The bill, which needs the approval of President Ahmet Necdet Sezer to come into force, amends a constitutional provision relating to independent candidates.
It was passed a day after the DTP decided to field independents rather than run as a party in the July 22 election to bypass the 10-percent national threshold that allows parties access to parliament.
Once they are voted in as independents, the Kurdish deputies can regroup under the DTP banner.
Under the bill, the names of independent candidates will figure on the same ballot paper as all the parties in the running, contrary to current practice under which their names appear on separate voting slips.
The measure is widely seen as a bid to obstruct voters in the mainly Kurdish southeast, where many are illiterate or do not speak Turkish, and are likely to have trouble picking their candidate's name from the long list of parties and other independents.
Many Kurds have become legislators in Turkey as members of mainstream parties, but pro-Kurdish movements failed to overcome the 10-percent national threshold despite usually dominating in the southeast, where they traditionally win the local elections.
Full article (Source: Kurdish Aspect)
Outgoing President Ahmet Necdet Sezer is a staunch secularist. Over the past five years, he has played an important role in striking a balance between the country's fiercely secular military and the Islamic-rooted government. Sezer vetoed several bills on the grounds that they violated the principle of secularism, and he also vetoed the appointments of at least 350 Islamist-leaning officials to key positions.
Turkey's political system is a parliamentary democracy, with power vested mainly in the government. But the president can veto laws after their initial adoption by Parliament, and then has the right to file an appeal to the Constitutional Court against legislation he opposes. He also appoints governors, ambassadors, police chiefs, ministry department heads and their deputies, senior judges, members of Higher Education Board, university rectors, and the head of the central bank. He is commander-in-chief of the armed forces. Turkey's military, courts and universities are traditional bastions of secularism.
Given this significant role of the president, the reaction to Gul's candidacy is not surprising. The AKP already controls parliament and the government. If it won the presidency, the party would hold all the key branches of power. Turkey would, practically speaking, be under one-party rule. Secularists have not welcomed the idea of directly electing the president, seeing the AKP's move as another threat to checks and balances. The influential business association TUSIAD warns that such changes should only be introduced following general elections, after comprehensive discussion and consensus among all the parties.
Finally, if you are interested in the Arab perspective of the issue, I suggest you to have a look at the Financial Times.