You do need more than 12 volts to charge a 12 battery. Also how do you know that your solar panel is producing even 12 volts? Just because that is it's rating doesn't mean it always produces that value. Do you have enough sunlight? Have you measured the output of the panel? Can you provide more information on the charge controller? If you did provide 24 volts to the charge controller, how much voltage will it apply to the battery which is important because 24 volts is probably too much. Your panel is rated at 12 volts and 5 watts. Thus, assuming it is getting sufficient sunlight, its maximum current is 0.42 amperes. At that level, charging a 4.5 AH battery, would take a minimum of almost 11 hours.
Firstly, the feed to the cameras:
I think, to be safe you should use a low drop-out regulator to feed your cameras - this takes care of slight overvoltages. The KA278R12C is a linear voltage regulator with very low drop out: -
Note that even when the input voltage is at 10V, the device is still able to ostensibly produce 10V at its ouput when delivering over an amp (6 ohm load). I suspect this device will be good enough to feed your camera system but I can't absolutely say because you haven't specified current. There are other higher power devices that would fit the bill.
Can I wire a load to my battery if it is connected in parallel with the charger?
If the battery is lead/acid and the charging current is significantly more than what the camera load takes when attached to the above regulator then yes you can. If the battery isn't lead-acid then we need to know which technology it is.
How can I add a solar panel + controller to the previous circuit?
Playing safe, you can use a relay circuit that activates the relay when the AC power is applied to the charger - the relay contact can switch the battery from solar charger to AC charger in a few milli seconds. Playing a little bit unsafe, it's likely that your solar charger will have a diode in its output that protects the battery from discharge when the sun doesn't shine.
This very same component probably can mean that you can connect the AC charger permanently to the battery (and solar charger) BUT, you may need to add a series diode\$^1\$ in the AC charger's output when AC is off and the solar charger is feeding juice to the battery; the AC charger's output circuits may be activated by the solar charger and it's difficult to say what will happen - worst case it might pop the output transistor in the AC charger - best case no problem.
However, the chances are likely that your AC charger (just like your solar charger) will be protected from reverse voltages when power is down (or sun is not shining). You need to check this.
\$^1\$The diode needs to be a low volt drop schottky type capable of taking the charge current (again, you haven't specified max charging current so it's impossible to say but there are plenty rated for 10A and 20A continuous usage).
Best Answer
What you refer to as a "battery" is actually a USB power bank, and you must not attempt to charge it with 12V!
The only safe method of charging that USB power bank, is a power source electrically equivalent to a USB port i.e. well-regulated 5V (I will see if I can find the minimum current requirement - check the USB power bank user guide for that information).
Edited to add: Based on the user manual for that USB power bank, it takes up to 5hrs to recharge, and has a 2200mAh capacity internal battery. Therefore it is unlikely to attempt to draw more than the expected 500mA from the external power source (which could be a standard USB port) when recharging its internal battery.
You mentioned "4200mAh" in your question - a typo of 2200mAh perhaps, as it doesn't agree with the webpage you linked?
Also note that not all (in fact I suspect a minority of) USB power banks can be recharged at the same time as also "charging" (i.e. powering) their output device. I did not find any mention of that feature on the web page which you linked - if simultaneously being charged and powering the Raspberry Pi Zero, was actually your intention.