I'm having the infinite energy argument in another thread "Show me your physics." I think the argument is that you should consider the Earth in an instantaneous frame reference, i.e. at rest. Therefore the concept of inertial mass doesn't arise.
You won't get any answer to any questions on space travel on this forum, as the stance is that it isn't possible so it doesn't exist.
I don't know what the responses (if any) to the tower or weighing machine will be, but it's usually that your experiment is wrong.
I'm sure they would love to further their research to cover these ideas more fully, but, as the wiki says, it's nigh-on impossible to get funding for FE research.
You have now travelled through the looking-glass. Welcome to Wonderland.