Can the contact on the condenser cause the unit to keep running when thermostat is turn off

If froze or stuck.
If you don't have 24 volts to the contactors(relays) coil, it should not be energized/pulled in/making contact

Some times the contractors get stuck, if you look at it it looks burn. Turn the system to cool turn the power to the A/H off ( only) and see if the condenser keeps running

Yes, the contacts on the contactor, which is what we call the large relay, have silver that wears away. When that happens the brass underneath welds together since the melting point is lower. Replace the contactor with the same or higher amp rating and the same coil voltage which can be 240 or 24 volts, but most often it's 24 volts in home units. The coil voltage is printed on the side of the coil. In some larger contactors you can replace just the contacts, but the small ones are very cheap being $5-15, but high quality ones can go very high up to $80-100. The cheap one is fine for your purposes. Just be aware of this fact. In AC parts houses look on the shelves to find the cheap ones in the showroom where mechanics get the ones to stock their trucks. In a home unit many are the cheap one contact set models, but it's best to change to a two contact model. The wires plug on the same way except between one set of wires there is a brass bar making electrical contact. When going to a two contact type just plug the wires on the same way they were plugged on the old one. Two contact models can save your compressor or fan motor one day. DrTom4444