Computers, monitors, and microwave oven power supplies can radiate out a fair amount of radio frequency interference known as RFI. This is also the same for the clocking circuits, and digital signals being used in the boards. Most modern appliances and devices use some type of switching power supply, and digital processing systems of some type.
Even if an appliance or computer is well shielded to block the RFI to an acceptable amount, there is always some that is able to radiate out. The AC line cord, and interconnect wires can also act as a sort of antenna, even though they are electrically referenced to ground, and may have RFI traps. The harmonics from the frequencies generated are very high, and thus the shielding that is used for these devices is not fully adequate, or able to do its job perfectly. The standards must always allow for some leakage, or the appliances would not be affordable, or practical to manufacture on a mass basis.
As for your phone, the amount of RFI you can have from a home appliance, or computer, can be strong enough to cause interference. This can be the same for most other communication devices.
I have seen a two-way communications radio cause interference to a computer that was about 15 feet away. I have also seen computers cause interference to cordless phones, and to ordinary radios.
As for having damage to a cordless phone, it would have to be exposed to extremely strong radiation. This radiation would have to be so strong that it would be dangerous for a person to be near by to the radiation source. I would worry more about the cordless phone causing interference to the computer. This may cause corrupt data if anything at all.
With a cordless phone, both the handset and base are transmitter and receiver devices. They are both susceptible to receive, and or to transmit signals, that can cause interference to other devices.
The bottom line is that I would not be worried about a computer, microwave oven (unless the phone is put inside), or monitor, or TV set causing damage to your cordless phone.