OEM size tyre is 155/80R13 which equals 578mm (overall height)
the ones you fit are 185/70R13 which are 589mm (which is 11mm larger in overall height). now if we put our thinking hats on we can clearly see that an increase of 11mm in overall height would mean 5.5mm on each side which would mean on a HIGHLY inflated tyre the car would be 5.5mm taller but since we are not filling the tyres to 90psi there will be some flex which will lead to only about 3mm ride height (maximum)
now go slap your tyre guy and tell him his daddy says to go get a job selling chuddis.
as for rims, yes they will add to the unsprung & sprung weight (unless you get some REAL good rims) and will therefore lead to a decrease in performance, heavier handling, slower braking and poorer fuel economy etc.
as for the cat, i've removed mine and many people have done it (without damaging the sensor) and none of us have had a check engine light. please go to a professional, these roadside ustaads are where they are for a reason, they are monkeys with basic tools.