There is no right answer for that. The bigger the better, ideally 4 ft long by the dimensions of your unit supply. If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79
Is this a new tstat? How about trying cooling with fan in on position , what happens? What is the model number of your indoor unit please. If you need further help, reach me via phone at https://www.6ya.com/expert/thomas_092728000e6acb79
If it’s a steady red light then that means it’s functioning properly. Flashing red is when there’s a problem. Check to make sure your blower door is on properly. If it’s not it is like a fail safe for the furnace to not start.
You did not post the model number but the compressor can come loose from the inside of the container that it is in. This can cause a noisy condition but it will not affect the performance or the life of the unit.