You almost never use the simple present tense, "I go out of the house". If you were using the verb 'go', you would use another form like "I'm going out of the house" or "I'm about to go out of the house". When you do use this, it could just mean you are going to the garden/front yard, OR it could mean you are completely leaving your house area and going to the shops perhaps. Similarly, you rarely say "I leave the house". You would say something like "I'm leaving the house" or "I'm about to leave the house" or "I'm going to leave the house" for example. When you do use this form, it's more likely you are going elsewhere (away from your house/property) to some place away from where you live.

Yes you can, but it does not neccessarily mean the same. 'Go out of the house' can just mean to go into your garden. "Leave the house' means that you are going somewhere else.

Yes. You can also say "I go out at...". It sounds more natural than "I go out of the house".

I would say no. It sounds really weird. Stick with "I leave the house at..."