In general panniers are more comfortable and efficient than carrying weight on your body. There are some things to be aware of, however.
Safety. Every time you set off, make absolutely sure that all the pannier straps are done up. Apart from things falling out, the last thing you want is a loose strap getting caught in the spokes. This can wreak a wheel, and a rider!
Regarding stopping distance, I don't think it makes much difference as the weight increases the friction between wheel and road. However, the extra weight does contribute something to heating the brake pads and rims/discs, but it's probably only an issue on long steep descents which are unusual on a commute.
Panniers getting in your way. Yes, aim to keep your heel clear of the bags. This can be different when the bags are fully-laden as they tend to bulge further than expected. Worst-case you can pedal with your toes pointed down to avoid heel-strike, but this isn't comfortable for long. If you swing your leg over to get on and off then definitely take a bit of extra care to avoid pratfalls. Also be aware the rear of the bike is slightly wider.
Left-right loading. Ideally it's nice to have them balanced, but unless there's more than 5kg difference between the sides, I'd say it's not really noticeable. So if all you're carrying is clothing and spare shoes, then it should be fine to take just one bag. However, if it's a stack of books consider two half-filled bags.
Vibration and bumps. In my wife's experience, laptops seem to suffer from vibration in panniers more than rucksacks/messenger bags. Hers acquired a serious soundcard issue after being bounced in a pannier back down a slightly bumpy road. I'm not talking about crashing or dropping the bag, just riding the normal bumps in British roads. Your road surface may vary. Putting sensitive kit on your body is less comfortable for you, but more protective for the kit.
Consider waterproofing. If the contents are sensitive to moisture (like the laptop), then you may want to double-bag unless you're really confident in the pannier's waterproofing.
Tire pressure. Adding weight to your bike means you'll need a slightly increased tire pressure to prevent pinch-flats, particularly for the wheel over which the weight is situated. There's another question with some more information on calculating the best tire pressure, but ideally it should be done per-wheel and adding panniers to the rear will make this more important.
The strap that runs from the middle with the hook on the end may be to wrap around the lower part of the rack (and possibly back up to the pannier). The aim may be to stop the pannier from swinging out away from the bike or from jumping off when you go over a bump, but in my experience if the strap is made of elastic it doesn't prevent this. The best design to stop the panniers hopping off is a clip which fully-encloses the top horizontal bar of the rack, as is found on Ortlieb and many modern panniers. If you want more detailed advice, post some pictures when you get the panniers back.