Led limiting resistor

[Demon]

I believe that the relay first will not withstand the 5 amps on the coil. ...

I would think that would depend on the rating of the relay.

...The second issue is that voltage is chopped by the SSR and heat controller, and the relay will come to a point when it will go crazy ON-OFF-ON , and the signal to CPU will be a pulsating one.
Thank you

That little detail might be a big problem.