It doesn't appear to have anything much wrong..
Please just do a reboot of everything first.. power everything off.. then restart the modem device.. followed 2min later by the TC.. then the clients.. tell me if that works.
In a computer.. open a terminal and type
traceroute 8.8.8.8
Copy and paste the result here.
Mine looks like this.
traceroute 8.8.8.8
traceroute to 8.8.8.8 (8.8.8.8), 64 hops max, 52 byte packets
1 gargoyle (192.168.2.254) 0.964 ms 0.814 ms 0.734 ms
2 adsl03.mel01.eftel.com (203.123.68.34) 60.839 ms 61.338 ms 56.881 ms
3 tge0-0-0-302.core0.mel.dft.com.au (203.123.68.25) 49.862 ms * 70.287 ms
4 202.61.240.78 (202.61.240.78) 67.530 ms 75.570 ms 58.717 ms
5 177.4.148.122.network.m2core.net.au (122.148.4.177) 69.985 ms 63.442 ms
225.2.2.123.network.m2core.net.au (123.2.2.225) 55.152 ms
6 74.125.52.41 (74.125.52.41) 54.587 ms
177.4.148.122.network.m2core.net.au (122.148.4.177) 53.918 ms
74.125.52.41 (74.125.52.41) 46.180 ms
7 * 74.125.52.41 (74.125.52.41) 47.425 ms
72.14.237.11 (72.14.237.11) 61.579 ms
8 216.239.41.5 (216.239.41.5) 86.470 ms
216.239.41.17 (216.239.41.17) 54.116 ms
216.239.41.83 (216.239.41.83) 57.729 ms
9 209.85.244.15 (209.85.244.15) 54.846 ms
google-public-dns-a.google.com (8.8.8.8) 88.162 ms
209.85.142.219 (209.85.142.219) 81.214 ms
The important part is in bold.. I can see that I have only one nat router.. what I am wanting to see is how many routers there are in your setup.
If you have no luck..
Just try what happens when you change from bridge.. which is what you are now.. to router..
So I want you actually to do a major change.. your current names can cause issues..
So please follow these instructions.
Start from a factory reset. No files are lost on the hard disk doing this.
Factory reset universal
Power off the TC.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the TC to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
N.B. None of your files on the hard disk of the TC are deleted.. this simply clears out the router settings of the TC.
Setup the TC again.
Then redo the setup from the computer with Yosemite.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg TCgen5 for basestation and TCwifi wireless name.
If the issue is wireless use TC24ghz and TC5ghz with fixed channels as this also seems to help stop the nonsense. But this can be tried in the second round. ie plan on a first and second round of changes to fix this.. hopefully.. I will point out other steps that can be round2.
2. Use all passwords that also comply with 1. but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
Run the setup wizard and if you need to put the TC into router mode try that.. so instead of bridge the network tab must show.. dhcp and nat.

The DHCP range should be different to your current one.. default 10.0.1.x will be fine.
It should then work fine..