Need more powerful wireless router for apartment

-50db is a good signal strength. The problem does not seem to be with low signal strength but most likely with interference. It looks like you are using the 2.4Ghz wireless band. On this band there are really only three non-overlapping channels. These are 1,6 and 11. You should always be using one of these channels and not any others as all the others overlap. Out of those three, channels 1 and 11 are most likely to have the least interference. The problem is that in a place like an apartment where the population density is high and many people have wireless, you end up with many people using the same channel. You can use an app like Wifi Analyzer that will show you all the networks around you and which channel (1,6, or 11) would be best to use. Also make sure your router is set to 20Mhz channel width on the 2.4gGhz band.
My recommendation, if possible, would be to get a router that also supports the 5Ghz band. This band has many more channels to use. But this would only be helpful if your devices can also use the 5Ghz band.
Here is a little analogy about Wifi and the problems with few channels in a highly populated area:
Think of wireless Ethernet like a CB radio (or walkie-talkie). Only one person can talk at a time and you can only talk or listen at one time but not both. That is exactly how wireless network radios work. So if you have 5 devices in your house using your wireless that is like having 5 people using CB radio's together. Only one person can talk at a time. Lets say your neighbors also use CB radios. Lets say they use the same channel as your CB radio's. Lets say they also have 5 people talking. Now you can only talk when the other 9 people are not talking. This is how you get interference from your neighbors on WIFI networks if they are on the same channel. Now your Wifi is encrypted so your neighbors can't get your data. So for the CB analogy, lets say your neighbors use a language you cannot understand and you use one they can't understand. So your conversations are still private but you have to share CB airtime with them because they are on the same channel.

Ok but -50 is good enough on almost all routers to get the maximum speed. So -34 or -50 should not make a difference. The router should be able to transmit at max speed. Most likely you are getting less interference in your living room and that is why you get better throughput. The best thing to do is download a Wifi Analyzer app. Then you can see if your getting more interference in the bedroom. The analyzer should not only show you all the other wifi signals going on but it should show you their signal strength also. In fact getting a more powerful router could possibly slow you down more. This is because many routers can adjust their output for best efficiency. If your router is very strong (loud) it will force other Wifi routers around you to also start transmitting louder which can cause you even more interference.
In my house my 2.4Ghz signal in my den is -54. I have moderate interference as I can see about 4 other Wifi signals on my channel (now they are fairly weak), but my throughput stays around 26Mbit/s. This throughput stays the same even if I move into the room with the router. If I had less interference I should be able to get close to 40Mbit/s.

The signal levels mean very little when you also have strong interfering signals. If you were to take 2 radios and play them on different stations and turn them both up very loud you would be able to hear both but neither would sound good because you are still hearing both stations. To continue this example if you were to stand closer to one radio you would hear it better but you could still hear the other radio. This is why your devices work better closer to the router.

You can't really fix this problem other than to try to avoid your neighbors by using different channels or bands. The only true solution is to move far way from everyone else. They do make some new paint coatings that have metal in them to block signals but in a apartment that is not likely a option.

Not legally. The transmission power is regulated by the government and all router generally transmit at the legal maximum. There are some you can directly import from china that can transmit over the limit. Still this is only have the problem, you would need large transmitters on your end equipment also since the router need to hear their signal. In most cases the router not detecting the end device is the much more common issue

lol scary how much we think alike!