Once your work has been published, we can discuss it here.
In the meantime, I suggest working through an introductory text on Special Relativity. Feel free to ask any questions in the relativity forum.
Galilean transformations are fine as far as they go. As Einstein (and others) have shown, they must be revised for high speeds. You won't get the correct (experimentally verified) results using them.
Not sure why you think that. Both mass (and thus weight) will increase with temperature -- but the increase will be quite small. (You can calculate it.)
@Mark44 makes a good point. It's a good idea to present your work logically so there can be no doubt about the steps you took. This is especially important if you must hand in your work to be graded!
(I knew what you meant, but still.)