It's perfectly fine to parallel Li-Ion batteries with one caveat. You want to make them non-removable. In other words, they should be permanantly attached in a pack. The reason is, like you said, the internal resistance is very low and high equalization currents can occur if the charge differs by much at all when initially connected. People do run removable batts in parallel, but you need to exercise care to avoid installing cells with a charge imbalance. There's also the risk of reverse installation which is even worse. A protected cell will keep anything ugly from happening whatever the case, but it's risky when using unprotected cells.
The hobby batteries (like the one you linked to) are always in series. I suppose you could take the pack apart and rewire it, but you don't need to do that. You can buy the cells individually. Hobbyking has individual cells by far the cheapest, but with a minimum 20C. You can find them anywhere from 2C to 20C through online shops like batteryspace.com, but they're a lot more expensive.
Single (or parallel) cells are much easier when it comes to built-in charging. I'm not going to get into what it would take with a series mod, it's just not worth the trouble. For series cells, just use a dedicated charger connecter. For a single cell, it's easy to install a USB charging module, but keep in mind, it's best to use a charging port like a wall adapter or powered USB hub. Even then, you need to make sure it can handle the current demand. Most computer USB ports have current limitations well below the the 1A or 1.2A rate a module may be able to supply. If you want to use a charging rate higher than that, what I said before still stands. You'll need a higher end charger with a dedicated connector. That's regardless of cell configuration.
One word of caution about high charge rates; the risk of a Li-Ion cell venting (going up in flames) increases exponentially with charge rate. The hobby guys charge their cells in a fireproof container even when using a 1C rate. If you actually do set up a charge rate at 5C, then you absolutley must charge your mod in a fireproof container.