The short answer: yes, it is very, very possible. By Europe, I'm going to guess you mean Western Europe since there is a long history of travel and trade between Eastern Europe and the Ottoman Empire and much of Southeast Europe was, well, Ottoman. I will scribble mostly on the English/British case since that is the one I know most about.

Arrangements: The Levant Company was set up in the 1580's as a chartered company by the English for trade with the Ottomans. There were regular ships carrying furs, spices, clothes, grain, etc., etc. going back and forth from London and other port towns to places like Jaffa, Constantinople, Cyprus, Chios, Izmir, etc. One could buy passage on one of these ships or just be an employee of the company itself, going off to make some money. Another option would be to go to Italy, either by ship or overland, and take a ship from there. Once you get to the Ottoman lands, to travel between cities, you'd might want to travel with caravans going from city to city since there are safety in numbers and they knew the routes. Another fairly common thing was getting a Janissary guide to take you through places safely, talk to the local traders for you, and beat up on anyone threatening you. Most of these interactions that you could do yourself would be in Italian, which was the lingua franca of the time and area. In terms of accommodation, it depended on the place (one must remember that the Ottoman Empire was huge and varied greatly). So, in some cities, like Izmir and Constantinople, there were English trading factories where you could stay. In Jerusalem, a popular site of pilgrimage and tourist-y shit, one could stay at a Franciscan establishment for pilgrims, at the possible risk of your own soul to Popery though. Along the roads, there were (sporadically) inns for travelers, although tons of people complained that the food was subpar and the inns were not common enough. One could also just knock on doors of non-hotel houses and offer money for a night's stay.

Chances of survival: I don't have numbers for you (and am unsure whether they exist or not), but there were a marked number of dangers that could mean if you went to see the Ottoman lands, you may not come back. There was the possibility of disease, especially malaria in many swamp, miasma-y parts of the land. Bandits and rebels could kills you (and thus the hiring of guides/guards by travelers). Bad food could kill you, etc. etc. Death was a real possibility. One interesting view into this is wager journeys in which there was a bet of no small sum that the travelers would make it to certain places and make it back alive.

Also, I wrote a damn thesis on this. I finally have found a use for this information, answering questions on Reddit! Much happy. If you want, I can recommend some travelogues of people (mostly men of English or Scottish background) who have made the journey and come back to sell stories about it. A good place to start about the English case is Gerald MacLean's The Rise of Oriental Travel: English Visitors to the Ottoman Empire, 1580-1720