Bizim Ev is the name of the restaurant and it does mean Our House in Turkish. Seray Zetas does serve other types of food but I'm sure your girls will find something they like amongst the Turkish food as well - chicken shish, pide (Turkish pizza), soup, salad etc. Our girls are only little and they love the food there.
Around 10% is the usual for tips for a meal, if you are just having a snack or drink just a few coins is fine. If you get a taxi anywhere just round up the fare for a tip.
There is a big market at Turgutreis on a Saturday, it is about 30 minutes on the bus. There is also a clothes market in Bodrum, above the bus station, on a Tuesday. Gumbet does have a small market on a Sunday, mainly fruit and veg but there are some stalls selling clothes, tablecloths etc. they are actually rebuilding Gumbet market this winter so it may be bigger this year. It is worth a wander round anyway even if you just want to get some lovely fresh fruit.
On the subject of food shopping, if you want to buy supplies for your apartment, food, soft drinks, beer, toilettries etc, then the best thing to do is jump on the dolmus (minibus), it will stop right outside Greenhouse, you just have to look out for a little green bus and stick your hand out. You can get this bus to the big supermarket, Carrefour, just outside of Gumbet and everything is a lot cheaper than the little markets in Gumbet. Then you can just get fresh bread and water from the local shops.
Yes, definitely haggle in the shops and , there is a post I did a few weeks ago called "Haggling for Beginners", which may give you an idea of how it is done. You can certainly try asking for a free drink if someone is trying to get you into their restaurant, a lot of places will offer a free bottle of wine (usually not the best but ok for free).
Kedi