Dear Bill, I'll try to answer your questions as numbered below..

1)If the unhappiness in your home has begun to be unbearable, you can of course leave it to stay in another appartment. But if you leave home in an incomplete condition and with an amiss reason(like flirting with another woman), this will absolutely be an disadventage for you while sharing the common assets of you and your wife while divorcing. What I understood from your message is that you can not abide to stay with your wife due to incompatibility anymore who you have already agreed on divorcing. So there's nothing that may cause to be a disadvantage for you, I think.

2)It doesn't matter whoever(husband or wife) seems to be the owner of an asset/a property in marriage, that will be decided to be shared between the parts by the Judge since it was purchased during marriage. There's only one exception of this rule for you to get the house entirely if you claim that you purchased it with your own personal money(like the money that you have been inherited by your relatives). You can not claim that the house is yours that you bought with your personal income. Because all the money you earn(even your personal income) during marriage belongs to your family, but not only you, according to Turkish Civil Code.

3)It's all the judicial discretion to decide who will have the custody of your child. There's nothing clear in Turkish Civil Code that gives exact clues whether to give the child to mother or father. The judge will make a decision about the custody of your child to give her the best future considering your and your wife's economical situations, her(child's) personality, social interests and even religional and national ideas. The judges generally give the custody of the children to the part who they feel themselves closer in the divorcement cases of international marriages. I don't know the details about your child but I can say that her custody may be given to you if she prefers to live in England rather than in Turkey(although the expressions of non legal-aged people(children) are disregarded).

King regards