I'm currently writing a library that encrypts sqlite database(It's hard to install sqlcipher on windows). Can I choose MIT even if I use pysqlite3 that is licensed under zlib?
If you have taken the pysqlite3 library and are modifying that to add your encryption feature, then you should keep the original zlib license, because it is just easier if a project is under a single license. And the zlib license is not that different from the MIT license anyway.
On the other hand, if you are pulling in pysqlite3 as a dependency into your project, then the zlib license places no requirements/limitations on the licenses you can choose for your project. So, you can definitely choose the MIT license in that case.
You can use MIT license for your code. So all users using your code must use it under MIT license, but if they touch that library, they can use it under zlib license.
Full package will be in mixed-license form (Some code is MIT, some zlib licensed). Executable will be under the zlib license, because zlib is more restrictive.
THIS POST IS NOT A LEGAL ADVICE