Do microcontrollers have a big resistance?
That is correct, in the sense that it can be thought like that for the sake of simplicity, but in reality there is no resistance at all, as it's a CMOS input which has an extremely high input impedance. It can be thought as resistor so large in value that it's not even there, and theory no current flows in or out that pin.
However, nothing is perfect, and there can be leakage current flowing in or out of that pin, but in worst case it is in the order of 1 microampere at 5V voltage, so it can be thought of as resistance larger than 5 Megaohms.
Typical values for pull-ups is a more broad question, as there is no single answer. Depends on supply voltage, switch current rating, level of coupled noise etc. So from 1k to 100k maybe.