Hello and welcome to the forum!
The Hotel Baba was closed last summer and no-one was sure whether it would be opening again this year, however the latest newqs is that it is being refurbished and will be open this season. As the season starts on 1st May the hotel should be ready by then, the majority of the major building work that has been going on should also be finished by 1st May to coincide with the beginning of the tourist season. If you are going with Thomas Cook they will be in touch if for some reason the building work isn't complete, they have been relocating people who are going the last two weeks of April to a very good hotel a little way off from the beach front ones so they aren't disturbed by the work. At the moment they aren't relocating anyone in May as the work should be finished but if you are worried give them a call as thay are aware of what is happening.
The hotel Baba is a very nice hotel, in a great location, right on the beach and also in the centre of the resort. there are plenty of very good restraurants in Gumbet, you will find every kind of food available for traditional Turkish to Chinese, Italian, Indian, Mexican etc. If you fancy trying some traditional Turkish food the best restaurant to go to is Seray Zetas, just a few minutes away from the Baba, it is very reasonably priced and the food is amazing. There are alos loads of bars ranging from laid back, quite places to busy, lively dancing bars. It will still be fairly quiet in may but you will find plenty to see and do.
The weather should be lovely, very warm in the day, maybe a little chilly some evenings so bring a cardi or light jacket just in case. It will be hot enogh to sit on the beach but the sea and swimming pools will be very cold! I always swim but some people wont go in.
Don't worry about Onur Air, i have flown with them and they are no different from any other budget airline.
I'm sure you will enjoy your first trip to Turkey and to Gumbet. If you want to know anything else just give me a shout, I lived in Gumbet for a few years so I know it pretty well.
Kedi