I need 6.5 digits
That means 6 and half characters? How can you have half a character?
If that means 6 characters before the decimal point and 5 after the decimal point, dream on. There is no way you are reading the accuracy of a resistor to 0.00001 ohms, no matter how you try. Perhaps you ought to observe the tolerance of the resistors you are trying measure.
every 0.1seconds at least
Sending 15 characters that often is not a problem. Reading the value to send, as you mechanically move the resistor in place could be.
not familiar with failure rate.
Have you ever pointed the remote at a TV, pushed a button, and nothing happened. Push the same button again, and the TV comes on? That is a 50% failure rate. Sending data is not guaranteed to be sent or to be received without getting mangled. Sending and receiving are not the issues, generally. It is interference that happens between the units that is a problem. Some radios handle interference better than others. Some frequencies are more prone to interference than others.
Budget is less problem BUT the transmitter package should be as small as it can.
But it is the sender that needs to measure the resistance, and send the data. That will require at least some external hardware.
You still haven't mentioned range. That is a critical factor. Across the desk is one thing. Across the room is another. Across town is in a league of its own.