In case 1, I would follow the STAR to the FAP, abiding by all applicable ALT and IAS limits. If the ALT limit is restrictive for GP intercept, I'd be asking for some descent (I'm assuming, in this case, that the ALT limit is imposed by ATC rather than the STAR, of course). At the FAP, I would then make the ILS approach.
In case 2, I would make the intercept on the currently assigned intercept heading and execute the approach.