Yes, bicycle shops generally provide repair services. A typical list of offered services includes regular service/adjustment (including safety check; and brake, drivetrain, and tire inspection); premium, and annual service, which is a more extensive tune-up. More specific repairs include drivetrain tune-up, brake system tune-up, flat tire fixes, brake repairs, cleaning and touching up the bike frame.
Change and a $20 bill: In case your cell phone’s battery dies, it’s nice to still be able to use a payphone if you need to. Also, the $20 is a great thing to have in case you lose your wallet or have some other mishap. I’d rather be able to sit in a coffee shop or fast food restaurant when it starts raining while I’m waiting for my friend or cab ride, and a hot cup of tea or coffee or the beverage of your choice and a snack makes it all the more pleasant. Just try to remember, this is for emergencies, and if you use it, replace it ASAP!
If you’re going to use the chain whip you just made, you’ll also need a way to get that cassette off. A lockring remover is a must-have; unless you use one of the shady removal methods I’ve seen on the internet—which I wouldn’t necessarily recommend unless you don’t care much about the condition of the wheel after you use them. I recommend Park Tool’s iterations here that cost about $6, but you’ll need to buy the specific one for your brand/type of cassette. (By the way, I’m assuming you already have an adjustable wrench laying around somewhere to use with this tool. If you don’t, well, you’ll need one of those too.)
Before I get started, I should mention that I never leave reviews. This is probably my first one on Yelp. These guys are just so great that I felt compelled to give them a shoutout. This is the shop I hoped to find when I began commuting two years ago. I'm a daily commuter and I love knowing that these guys will help me almost anytime that I need it. Andy, Jake and Brad listen and make sure to help me as best they can and are always speedy about it. Additionally, they encourage me to do my own work on my bikes when I have the time/when they know I'm capable and I really appreciate that encouragement. These guys will give you their best and provide some laughs as well. Couldn't recommend them more!
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.
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.