How can this problem be fixed?

You will need to tell us more. What model radios are you using? Can you hear others talking but not your friend with the other radio? If you can hear other talking, the problem my be a defective transmit circuit on the friends radio. If you can not hear any one, you may a a defective receiver or broken antenna. Can the other person hear you?

If you want to speak to the recipient before sending a fax, or if the recipient does not have a fax machine that can receive faxes automatically, send a fax manually after speaking to the recipient on the telephone to check whether the recipient can receive faxes.

1. Make sure that the machine is turned on.
2. Press the FAX button.The Fax standby screen is displayed.
3. Load the documents in the ADF
4. Adjust the scan contrast and resolution as necessary.
5. Lift the handset of the telephone connected to the machine.
6. Use the telephone to dial the recipient's fax/telephone number.
7. Speak to the recipient.
   When you hear a high-pitched signal instead of the recipient's voice, you cannot check whether the recipient can receive faxes. If you want to stop sending the fax, replace the handset. If you want to send the fax, go to step 9.
8. Ask the recipient to set the recipient's fax machine to receive faxes.
9. When you hear a high-pitched signal, press the Color button or the Black button.
   Press the Color button for color transmission, or the Black button for black & white transmission.
   
10. Hang up the handset

CTCSS is a subaudio (<300Hz) tone that is broadcast when you transmit on a radio. If another radio is set to receive that tone, then the squelch will open and he will hear your transmission. Having said that, any other radio that does not have CTCSS set at all will also hear your transmission, so all it does is for the receiver to hear less of others talking. DCS is the same except that CTCSS sends out a continuous tone, DCS sends out a string of tones. This allows more "channels" to be allocated, but still ,everyone is using the same frequency

see:
CTCSS DCS

replace this unit worn out!

"cannot send or receive faxes to one particular number, but is able to send and receive faxes with other numbers"

If your machine can receive a fax transmission from one number, it will receive from all numbers.

If your machine can send to all but not to one particular number, please check that there is a fax machine there to receive it.

You can try to send manually and listen for beeps from the other fax -if one is present- then push the START button to initiate transmission.
If their machine is in working order, the transmission should start. (After the initial 'handshake' of course.)

Maybe your microphone of the phone doesn't work.Send your phone to the shop nearby to fix it.

In that case you have a fault which is not user-serviceable. Your phone sends and receives on two separate frequencies. The receiver side of things is working, but the transmission side has failed.

There are a number of possible causes, some are easy and cheap to fix, others may mean that the phone is beyond economic repair. If your phone is still under warranty and has definitely not suffered liquid damage then you may be able to get a free warranty repair. In practice, it's a phone which retails for only £65 or so, so it's more likely that the phone will simply be exchanged under warranty. The company sends out a bare phone (no battery, battery cover, etc.) and you return your phone in the same condition.

(2) Service error codes
on.
- Logic board
#001 TX Document jam
#003 TX / RX Document is too long, or page time-over
#005 TX / RX Initial identification (T0 / T1) time-over
#009 RX Recording paper jam, or no recording paper
#012 TX No recording paper at the receiving machine
#017 TX Redial time-over, but no DT detected
#018 TX Auto dialing transmission error, or redial time-over
#022 TX Call failed (no dial registration)
#037 RX Memory overflow at reception of an image
#085 TX No color fax function supported in the receiving machine
#099 TX / RX Transmission terminated mid-way by pressing the Stop/Reset button
#995 TX / RX During TX (sending): Memory transmission reservation cancelled
During RX (receiving): Image data received in the memory cleared
Error code TX / RX Meaning
##100 TX Re-transmission of the procedure signal has been attempted the specified number of times, but failed.
##101 TX / RX Sender's modem speed does not match the receiving machine.
##102 TX Fallback is not available.
##103 RX EOL has not been detected for 5 seconds (or 15 seconds in CBT).
##104 TX RTN or PIN has been received.
##106 RX The procedure signal has been expected for 6 seconds, but not received.
##107 RX Fallback is not available at the sending machine.
##109 TX After DCS transmission, a signal other than DIS, DTC, FTT, CFR, or CRP has been received, and re-transmission of the
procedure signal has been attempted the specified number of times but failed.
##111 TX / RX Memory error
##114 RX RTN has been received.
##200 RX A carrier has not been detected for 5 seconds during image reception.
##201 TX / RX DCN has been received in a method other than the binary procedure.
##204 TX DTC has been received even when there is no sending data.
##220 TX / RX System error (main program hang-up)
##224 TX / RX An error has occurred in the procedure signal in G3 transmission.
##226 TX / RX The stack pointer has shifted from the RAM area.
##229 RX The recording area has been locked for 1 minute.
##232 TX The encoder control unit has malfunctioned.
##237 RX The decoder control unit has malfunctioned.
##238 RX The print control unit has malfunctioned.
##261 TX / RX A system error has occurred between the modem and the system control board.
1-7

(2) Service error codes
on.
- Logic board
#001 TX Document jam
#003 TX / RX Document is too long, or page time-over
#005 TX / RX Initial identification (T0 / T1) time-over
#009 RX Recording paper jam, or no recording paper
#012 TX No recording paper at the receiving machine
#017 TX Redial time-over, but no DT detected
#018 TX Auto dialing transmission error, or redial time-over
#022 TX Call failed (no dial registration)
#037 RX Memory overflow at reception of an image
#085 TX No color fax function supported in the receiving machine
#099 TX / RX Transmission terminated mid-way by pressing the Stop/Reset button
#995 TX / RX During TX (sending): Memory transmission reservation cancelled
During RX (receiving): Image data received in the memory cleared
Error code TX / RX Meaning
##100 TX Re-transmission of the procedure signal has been attempted the specified number of times, but failed.
##101 TX / RX Sender's modem speed does not match the receiving machine.
##102 TX Fallback is not available.
##103 RX EOL has not been detected for 5 seconds (or 15 seconds in CBT).
##104 TX RTN or PIN has been received.
##106 RX The procedure signal has been expected for 6 seconds, but not received.
##107 RX Fallback is not available at the sending machine.
##109 TX After DCS transmission, a signal other than DIS, DTC, FTT, CFR, or CRP has been received, and re-transmission of the
procedure signal has been attempted the specified number of times but failed.
##111 TX / RX Memory error
##114 RX RTN has been received.
##200 RX A carrier has not been detected for 5 seconds during image reception.
##201 TX / RX DCN has been received in a method other than the binary procedure.
##204 TX DTC has been received even when there is no sending data.
##220 TX / RX System error (main program hang-up)
##224 TX / RX An error has occurred in the procedure signal in G3 transmission.
##226 TX / RX The stack pointer has shifted from the RAM area.
##229 RX The recording area has been locked for 1 minute.
##232 TX The encoder control unit has malfunctioned.
##237 RX The decoder control unit has malfunctioned.
##238 RX The print control unit has malfunctioned.
##261 TX / RX A system error has occurred between the modem and the system control

You will need to send you phone in for repair since the mic is part of the mainboard and will need to be fixed by tech or they will probably just send you another phone.