As you mentioned, it is surprising how often you can get multiple flat tires on while riding, particularly on longer sprints. The tip about bringing a patch kit in your bike repair kit can be incredibly helpful if you’ve already had one flat tire. I agree that all you listed seems like an awful lot to carry, but it’s always better to be safe than sorry, isn’t it?
Whether you ride a single, 7, or 10 speed bike or anything in between, you will need a slightly different chain. The major difference is that they come in varying widths to accomodate the different spaces between the gears, but quality of construction is also a factor in choosing a chain. Inspecing the chain should be a part of your regular cycle maintenance procedure- It’s important to keep a chain well lubricated, but oil will also attract dirt and so different oils for specific riding conditions are available. Remember to clean your chain regularly to get the longest life out of it and the gears.
In addition to the Rema patches, put a new tire tube in your kit. The best method for dealing with a flat roadside is to swap out the tube and save the task of patching for later. If you’re not sure what size your tires are, it’s printed on the sidewall of the tire. This inner-tube buying guide has some photos of where to look. What brand is almost irrelevant as many tubes get manufactured in the same place, so whatever your local shop has behind the counter for under $10 will work fine. The only reason to spend more would be to save weight.
The Pedro’s lever slipped only once throughout testing, though that may have been my fault because I was spaced out after changing 16 different tires. So they’re not foolproof, but they are far and away more reliable than the next closest competitor, from Park Tool, because the small, rounded tip on that one is hard to keep seated under the tire. Not impossible, but I wouldn’t choose it over Pedro’s.
A wrench that fits the hub nuts: If your bike has quick release front and rear wheels, you don’t need this, but if you have an internal hub on the back, such as the NuVinci, a wrench that fits is a great idea. 99% of the time, this is a 15mm wrench, but you should check your bike. A 6 inch adjustable wrench can also work, but it will be heavier, and when using an adjustable wrench, you do need to take more care to not round over the nuts. A fixed wrench is the best choice. Some multi-tools have a 15 mm wrench built in, but again, if you have limited hand strength, something with more leverage is a great idea.