does cables exist to connect smartphones to modems/routers ?

Never heard of one. Why would you want to?

Yep.

http://www.ebay.com/bhp/micro-usb-ethernet-adapter

Yes, but it would be a lot more convenient to connect wirelessly. Is there a reason you need ethernet? Is your router not wireless?

I haven't done this, but if you have wireless and connect with ethernet, you might get a conflict. I say that only because when I put a wireless nic in a computer tower and install the driver, I have to go into device manager and disable the ethernet port and enable the new wireless nic or too often the computer will keep hunting for an ethernet connection and not connect to the wireless.

I seriously doubt if the mini or micro female usb port on most smart phones would have the software to use it as a LAN

Until someone posts here that they can do it, I would vote for a NO GO

There are apps to share files between your PC and your phone via Wifi if that's what you're after.

I connect to the Internet using a cable modem (I think so). I use a wifi router to connect to the cable modem. As usual being lazy, instead of connecting my 5 year old laptop to the modem or router, I want to connect my Android devices to test my connection speed. I have 4 Android devices.

I connect to the Internet using a cable modem (I think so). I use a wifi router to connect to the cable modem. As usual being lazy, instead of connecting my 5 year old laptop to the modem or router, I want to connect my Android devices to test my connection speed. I have 4 Android devices.

Then connect them all wirelessly that is the speed you want to check anyway

Unfortunately TRUE mentioned that the actual speed can never be attained using wifi; my dual mode router can boardcast 2.4 and 5 in addition to granting restricted access to guest.

Unfortunately TRUE mentioned that the actual speed can never be attained using wifi; my dual mode router can boardcast 2.4 and 5 in addition to granting restricted access to guest.

Did they mention to you that Wifi speeds generally far exceed internet speeds anyway, so that isn't the bottleneck.

if your work scenario is 4 android devices accessing the internet at the same time, you do need to test this configuration actual in your setup. then you know the bottleneck if your wifi router of the TRUE modem, or the download/upload traffic. then you adjust your setup accordingly.

as Chicog mentioned, the wifi speed (assuming you are on b/g/n) by far higher than that of the internet line, especially here in Thailand.