Up to 128G. A 64G memory card is included in the package. 

Built in. Only need sun or plug in charger ( it comes with one) to power up. 

Depends on what you mean by direct sunlight. If you mean the filter pointed directly at the sun, and you are worried about lens flare, well it wont stop that. But if you mean using it out in bright bright sunlight all around, then it works great. I'm a member of the Longview Film Club. We shoot indie short films, and use these for all of lenses and cameras. It's a must when shooting outside under almost any conditions. Makes it possible to get nice Depth of Field even on a sunny day. 

I believe so, however, I have not set mine up yet, so I can't say for sure. 

hello ,you can use ie take picture of the sun, but not for the solar eclipse