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?
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.