I am looking at buying a battery pack like this, or this. If you can't open the links, those are simple Li-ion battery packs (11.1v and 7.4v respectively).

Which will be charged with this "smart" charger.

But for charging my phone/other things, I was thinking of using this UEBC (is it just a switch regulator?).

But how do I connect them so that when I get home I can plug the battery pack into the charger, and when I'm on the road I can use the switch, without having to move any wires around? I'm assuming there is a very simple way of doing this, but since I have never touched a circuit before...

I am happy to read anything in the circuits guide that you point me to, as I have done so before and found it very helpful.

Should my first question have been whether or not I can even use that switch with my battery to charge a cell phone? I just figured that since it says its output is 5v and 4A I should be good.

 

There are a few things about batteries you need to know first.

Lithium Polymer (Li-Po) batteries are VERY finicky about how they are charged and discharged. They are unforgiving in this, resulting in flames or explosion.

Some packs have a charge control circuit built in (more than 1 contact per cell), such as cell phone batteries. That, however, doesn't mean a voltage can be applied and it will charge correctly. The circuit only prevents dangerous currents, not charging that will shorten the life of the battery down to maybe 3 uses.

The Battery Eliminator Circuit you posted is just a power supply for running Servos and Receiver on an electric vehicle from the large batteries supplying power to the motor(s). This is only a power supply with a 3A output, which is NOT suited for charging a battery. That supply could possibly be used to power a Li-Po charger.

You'll need to look at charge control ICs. Finding a standalone Li-Po battery charger that has sockets to accept your battery will be the most headache free method, though it is more expensive (due to the extra circuitry to monitor and charge the batteries properly).