Determining WiFi Quality

As far as the circuits go: there are 3 wires (plus ground).  2 "hot" and 1 neutral.  230vac between the 2 hots and 115vac from 1 hot side and neutral.  So, what you call a typical household "circuit" is one of those.  
Your test with the night lights won't tell you which "hot" is being switched - it will tell you that the outlets are on the same breaker and, thus, on the same side (of many others on that side).  But this is likely to be a sparse population of outlets and likely not so far apart from one another physically.

A modern breaker box will generally alternate single breakers between one hot side and the other.
(So, when you see a breaker for a stove, oven, air conditioner, etc.  it takes up two positions and picks up both hot wires for 230vac.)
The breakers are in 2 columns and the alternation is down each column.
So, if all that's the case, then you might want to pick a pair of outlets that are some odd number of locations apart on the breaker box.
The whole point of doing this is to get the best signal and not lose signal through the transformer which is the only common connection between the legs or sides.  It may not be the most important test.  You might as well trust the lights on the extender.

As soon as I pair the two TP-Link devices I loose all WiFi and need to restart my Bell modem to get it back."

Now this is something else altogether.  The wireless capability that's build into the "far end" of the extender pair (you DID plug the wireless one at the "far end", right?) is just a simple wireless access point.  
Does the wireless stop working when you plug in the extender at the far end?  Or does it stop working when you plug the camera into it?  The specs you sent say: RJ-45 10/100Mbps adaptive network card and NOT wireless.

I presume the "wireless problem" is with other wireless devices in the apartment now?  
Might it be that the extender and the current access point are on the same channel?  They are likely much better off being on different channels so they don't interfere with one another.  If that's done then there should be no problem.

If it drops down to 5Mbps, is that only the furthest room away from the modem? Or also right next to the router?

Some cheap cams, contain cheap electronics which cause slow operation.

Reset the TP-Links, do NOT use the WiFi clone function, just use it as a separate AP first. Test now.

Using Powerline products in one same circuit or not, isn't always possible. You buy this to cover more distance with your networking. Just test many locations that seems logical. If the same circuit is still to close to the source, it beats the whole purpose of having the Powerline solution? Just test it where it makes sense. If it works, keep it. If it doesn't return it to the shop.

WiFi "quality" when defined as "throughput" in an apartment building in my experience is spotty at best, because everybody else in the building also has a WiFi router, and the routers are all (in the best case) fighting over a temporarily open channel, and (in the worst case) all sitting on the default channel and trying to shove an apartment building's worth of data down one channel.  It is a recipe for disaster made worse in a city where there may be another apartment building next door, and next door, and next door.

Kimputer's comments on HomePlug are apposite.  When it works, it works well.  But do not attempt to use it as WiFi augmentation, particularly not in this situation.  Use it as a wired Ethernet replacement so you are not fighting both power line data transmission and WiFi crowding.

Not all HomePlug products are identical in reliability or performance, which makes no sense at all because they are all built on the same chipset.  If product A from vendor LS, doesn't work, try product B from vendor NG instead.  And try older versions of HomePlug products as well.  A reliable 40 Mbps from an obsolete PL200 is better than an unreliable 200 Mbps from a brand-new PL500.

Finally, where it is possible, stick to wired.  It always works at full speed and is unaffected by external issues other than the ISP going down.

My experience suggests this:

Always use wired whenever possible.  Use actual CAT 5E or simlar whenever possible to extend the network across the living spaces.  
In many cases, extending wired with powerline extenders works well and still avoids the number of variables involved with wireless.
I've found a few situations (inlcuding in my own home) where powerline extenders don't help / don't work.  They are worth a try but can't be relied on to be a "solution" in any particular case.  If not, go back to cabled connections and, reluctantly, consider wireless extenders.  
Note that even wireless extenders can terminate with RJ45 ports.
So, you might start with wired, go to extenders of any kind and end up with wired again.
If that works then you can always add wireless access points.

If wireless capability is needed (such as for cell phones) then condsider the wired connections FIRST.
Then place the wireless access points at the end of the *wire* (as above)  that's nearest to the point of needed wireless service.
I reserve application of wireless extenders as a rather last resort.  These should be placed "half way" (a loose term) between the wireless source and the wireless need and NOT closest to the wireless need as some might assume.  "Half way" means that the loss from the source is about the same as the loss from the extender to the point of need. ( I rarely use these any more.)  So, just as an example, if you have to work through 2 walls then you might place the wireless extender between them.  
With wireless "line of sight" is the best you can do - like with a flashlight.  So, consider using hallways as an attractive path.

I have had poor experience with automatic channel selection in wireless.  But this information is somewhat dated.
You might use something like inSSIDer on one of your computers (with wireless capability) to see which channels are already in use and try to avoid those or at least the stronger ones.  If you are situated in a place where the wireless channels are quite loaded and varying then *maybe* automatic channel selection can help - but I rather doubt it.

I find a "Wi-Fi Analyser " app for Android (or IOS) mobile quite a useful tool for checking out signal strength and quality whilst moving around the home.

​WiFi Analyser for Android.​​​

If I were to return everything, is there an WiFi Extender that can be connected with Ethernet and not depend on circuit? Is there a camera with audio that is Ethernet wired?

WiFi Extender with Ethernet, is .... basically... an Access Point (so just get a new Access Point). HIKvision has many camera's with Ethernet and mic. Ex.: https://www.hikvision.com/europe/products/IP-Products/Network-Cameras/acusense-series/ds-2cd2346g2-i-u-/ 

Is Access Pont a Router? If so, would it be correct if I ran an Ethernet from my Primary Router or Switch to the "Internet" port of the secondary router (AP) and set up the same SSID???

A router has more functions than a more "dumb" access point. Some routers have an access point mode. Hence access points are cheaper than routers. But if you have a router anyway that's doing nothing, you can use it. If no access point mode is available, just disable DHCP, and use ONLY THE LAN ports (not the WAN/Internet port). Then it's basically an access point.

I decided to take a step by step approach to figure out all of this.

First of all, I placed the camera right next to my router and I still get 50-55KBps, but the quality is slightly better, but there is still about 10 sec lag. Couid it be that this is the maximum capacity for this camera?

Secondly, can anyone tell me why my WiFi drops as soon as I link up the two TP-link devices?

Thirdly, before I used to have Bell WiFi pods where the WiFi signal bounced off one another, but they dont offer them with my current plan. Is there anything like that on the market that does not depend on the electrical circuit, but it just bounces the signal?

can anyone tell me why my WiFi drops as soon as I link up the two TP-link devices?

There are two possibilities:
1) I believe I already mentioned channel selection / interference but, while possible, isn't very likely to be seen with the symptoms described.
2) an IP address conflict could cause something like this