I'll identify the radios to help me answer your questions...
The 6-Watt radio - not unlike the 6 Million Dollar Man - not adjusted for Inflation...
(...when you look at it that way, its' still about $6 bucks...)
Considering the Age of this radio - several things can be wrong with it.
If it's more than `10 years old, it will need a lot of component replacements, mostly of Electrolytic capacitors inside that radio Many short out as they dry out. Muddy Audio and a heating up audio chip (that flat pack with a row of pins) and if you aren't careful - and neglect to replace these older caps - they can further damage the radio.
Check the PA CB switch as well as their rear panel jacks. I mean get an extension speaker - and plug it in. Check the Audio quality of the internal speaker compared of the external one - if the internal sounds "fuzzy" or pinched, rattler - it may have a bad core (speaker) coil that renders the speaker unable to vibrate - it easier to replace it.
Microphone audio too, PA side using the extension speaker - adjust the volume control to lower the volume and also check the Mic Gain (Dynamike) control - listen for scratchy static-y sounds as you rotate controls and try to adjust the volume. Intermittent and Noisy usually means - dirty wiper contacts. That means the radio will have to be cleaned up for the pots that handle the radios functions need cleaning.
Barely Showing Modulation...
Again age of thee radio tells me the Capacitors need work but there's more - this one may be damaged requiring more work to it.
The Modulation (Reactance) Transformer is weak. May also mean that it has a blown or shorted windings. Means replacement is in order.. You can confirm by using an external speaker. IF the external speaker sounds "normal" then the INTERNAL speaker is bad and should be replaced.
Weak output usually means the Final or the circuits that send power to the Final - need to be checked. This goes back to the above statement about the Transformer - for if it is a shorted or open winding in it's internal core - or shorted out - means damage and if the Final is bad, it too needs replacement..
The above are just approximations and assumptions based upon several factors of experience and age, and routes to troubleshoot based upon your described symptoms.
You'll need some tools to help you fix these and then it is still not a guarantee it will ever work normally. For radios that have shown signs like you describe are usually too far gone to offer you a SIMPLE GO HERE TO FIX THAT kinda' scenario. Many of these orphans (If I can say it) are lost causes because there are usually more problems in them that once you fix one symptom - others take their place and eventually you'll get to spend way too much time tinkering, replacing and in parts swapping - just to repair the radio. Moreso than it's worth.
But that is not to say you can't learn something from attempting to fix these.
I've had situations where two radios were recombined into one to make one workable and salvage the other for parts to allow the other one to live. Not the best thing in life but it does keep one radio going versus having two dead ones.
I'll stop here and see if others can provide good ideas on how to proceed...