Christ, I hope this is your own money.  That's a pretty reckless decision.
As far as I know, it's a safe way to store crypto.  I haven't seen any reports of serious problems yet.  But there are a couple of potential problems:

1.  If someone has access to your computer, unless you protect it properly, they may be able to steal your funds.  This includes malware as well.

2.  Exodus is not open source, so it's not as easy to check it over for malicious actions by the developers.  In the context of a cryptocurrency wallet, this can be quite important.

Basically, it's fine, but it might be good to try the reference client for whatever coins you're interested in.

Why is it reckless? Super smart if you ask me.

I assumed that it would be more of your savings than that, since most teenagers don't have access to $10,000 of their own money.  But 10% is fine and it could be an interesting experience for you, I suppose.
Blockchain.info doesn't have access to your private keys.  But your concern about web wallets is understandable.
It's unlikely, but there is some risk.
Knock yourself out.  If you want more advice about that, head to the altcoin boards.

It depends. It's reckless if the $1000 is like the majority of OP's savings. Also, it's also quite reckless for OP to invest $1000 but not invest a percentage of it for a hardware wallet. He/she's taking unnecessary risks. I'd personally buy one just for peace of mind.

bright idea being a teen you have a plan to your future choosen investing int bitcoin are very wise decision at your age, i support with your decision but you need to place your bitcoin in a very safe wallet,
i suggest with you store your investment in electrum this i know one of safety wallet, but if are sure in exodus to store your crypto make sure you have an secured privateley and do not share to the another people for the security of your coins.

If you want to invest in cryptocurrency there are a lot of choices for you to choose cause there are more than 1300 cryptocurrency on the market. But if IMO if you want to invest in long term about 5 - 10 year I think you should choose BTC or ETH only, with 1000$ it's not enough to buy 1 BTC so I think the better option for you is ETH. From the early of this year ETH price has increased more than 4000% so it has very good potential in the future as Bitcoin or maybe better than Bitcoin.

Beside you the wallet, Exodus is a good one but it's not totally secure, if anyone can be able to hack your wallet seed or private key, it'll be terrible cause they can steal all your cryptocurrency. Coldstorage wallet is still the best, the most secure wallet although it's affected by a lot of factors outside but I think you still should choose it.

I personally think there is any problem in saving your bitcoin with Exodus but is that since you have of investing for a long time period why don't you invest some percentage of your capital into some other altcoins and some new projects during their Initial coins offering because that will bring more return on your investment.

When I was your age I invested some money to buy Bitcoin. I think it is the only genuine crypto-currency potential to increase in value for next coming years. If you want to spread your money over more currencies then I would chose Litecoin, it's identical to Bitcoin but has 4 times more supply, 4 times faster block times and it's not over populated so the transaction fees aren't that high. 85% Bitcoin and %15 Litecoin or less is a good choice. The safest way to store your coins is a paper wallet. After buying your coins using an exchange you can easily withdraw your coins to a paper wallet. Then when you feel you want to use your coins, you just import the private key to a desktop wallet. I don't think a computer is much saver to water or getting stolen. Make sure you make an extra copy and hide them on different places.

I recommend to not keep your money into an online wallet for a long time because online wallets are the most vulnerable to hackers and also the easiest to hack. Everyday,hundreds of wallets are hacked and on a long term your wallet could be one of those.
Invest some money (50-100$) and buy an hardware wallet where you save you seed and all the informations about wallet, and also make a few copies in case the first is lost.Hardware wallet is easier to use and a lot harder to hack, maybe even impossible if you are careful.
Regarding what coins to buy, I say bitcoin in a big proportion(80-90%) and ethereum(10%). It think both of them are going to survive overtime and the price will increase. It is your choice to choose what you spend your money on.

with 1k $ to invest in a cryptocurrency so still profitable, by choosing cryptocurrency wich to buy. but , if invest 1k $ from now in bitcoin ,growth profit so small and have big risk. but if you still want to invest in bitcoin, I suggest to make your own mining rig.