I think free speech is absolutely key for a free democratic society. This means that people should be able to say anything that they want about their leaders- whether it is in private or in public. If the people of Turkey are not able to openly insult their President, this is not a good sign of their human rights and freedom.
Yes, people in Turkey should be able to openly insult their president. If you cannot criticise your government, you are not free. In a free society, Freedom of Speech is the most important right. If we cannot have open discussion and debate, only one opinion will be heard. This is tyranny.
Any time that a politician, no matter what country they are from, does something wrong or questionable, then the citizens of that country have the right to question them or even insult them if they have done wrong against the country they were supposed to be serving. It is a leader's job to serve their people and if they fail at that then they should expect some backlash from their people.
Yes, people should be able to openly insult their president because criticism prevents the president from performing acts that are in not in accordance with a nation's principles and beliefs. The people elected the president to his office, and they should be able to openly voice their insight if they feel the president isn't doing a good job.