Tyre restrictions?
 

I know we cannot use things such as mini pins, but is there any other restrictions on tyres types? i.e. are rubber slicks permitted?

Rubber tyres are ok
Some people use carpet dragons
As long as it doesn't damage the carpet it's ok

Torn between getting some rear, softer foams, or changing to rubber slicks.

It's between a Sorex XG-28JB set of 4 or a pair of HPI RS4 35 shore foam tyres to go with the 45 shore HPI foams I have already

The foam will handle better but the rubber will last longer it all depends on your driving style which you prefer cannot really advise either way it's trial and error
Until you find what best suits you and the car