I finally found the answer! After hundreds of white-boards filled, I am sure I can build the first time machine! ...Wow, it will be expensive, and time consuming... and actually pointless... Unless, maybe...
My character is about to build a time machine, she has solved every little issue that she would encounter, she has all the blueprints, but now she is in doubt...
According to the theory (which is acceptably true in the universe(s) she lives in):
- You can not send mass in time, only waves, transporting only energy (e.g. encoded signal, so SMS and mails are allowed) and,
- When one sends waves in time, it does not alter the universe one lives in, the wave travels to an alternate time line where this wave is received (multiverse theory?). For example, if she sends to herself an email containing lottery numbers, she is sure that the "she" from an other time line would become rich, but the actual she (who sent the email) would stay poor with a huge Internet bill. Same happen if she tries to send energy in the future (Paradigm 2 on this question)
- Finally, she can not send signals to a date before the construction of the time machine. The time machine acts as a receiver as well as a transceiver.
The constraints are largely inspired by the anime Stein's Gate, if it could help to have a clearer view.
What features could be added to the time machine to make it beneficial knowing the time travel constraints stated before? Because, as stated before, sending back the lottery numbers would not make her richer.