Altcoins are decentralized, opened sourced, digital currency.
In some ways Altcoins are like Bitcoins, however, some are completely different, some like Ethereum are more blockchain based operating systems than they are cryptocurrency, in fact you can make cryptocurrencies on Ethereum, Namecoin as well is different its a DNS on the blockchain and more altcoins will be developed with even more interesting features.
Bitcoin is slow due to the way the blockchain was designed and transmitted, your fees matter, the lower the fee, often the slower the transaction, Altcoins don't all operate like that, some are extremely fast and used by Banks and other financial services.
You can store data and do many different things using the blockchain, voting systems and person to person lending concepts are being developed as we speak, game concepts using cryptocurrencies in games as well using the blockchain to store game data are also being worked on.
The blockchain is really a database that only the cryptocurrency it was developed with runs on, unless otherwise developed, but can also be duplicated thousands of times across networks.
Cryptocurrency can be faster to transact, safer and can also have added features that can benefit the user, your paper money collects germs and is more easily stolen.
No, The majority of altcoins are real and legit, however just like any other idea, ideas to working concepts, don't always pan out and scams are around as well, it's always best to research before jumping into anything.
Yes, just like fiat money, Tide detergent, tobacco and other things have been. Mainly bitcoin was used because some people thought their transactions would be hidden if they used it with other services, however that was not the case always and people got caught.
You use the cryptocurrency wallet for the altcoin you want to use and all transactions and storage happen through the software, you often have a password and private key to identify you to your wallet, there are even hardware wallets, however they still need to be online to work.
You can either mine cryptocurrencies or buy Bitcoin or Altcoins on exchanges, from a person selling them, from a coin faucet and from selling something for altcoins.
Cryptocurrency Mining uses software and hardware to solve math problems or combine computing power or really whatever the developer set up to earn their cryptocurrency.
More and more popular places are accepting bitcoin, and altcoins in various forms are being accepted but not altogether, there are sites you can buy giftcards to many popular stores for altcoins and even gambling sites with the promise to get rich quick.
You use the cryptocurrency's blockexplorer and enter your transaction id, or wallet address to display your transactions.
Some cryptocurrencies as mentioned before are more platforms for other applications to be built ontop of than currencies, some are smart contracts and others are website servers, it's really up to the need you're addressing and the creativity and imagination that will limit your design.
Some exchanges did spring up with the intentions of stealing money, others weren't handled well and some had issues and corrected them, many of the exchanges now are regulated to a degree they are liable in court and as a result conduct themselves in a professional manner, however you'll always have some trying to get rich quick.
A few websites and exchanges sell stocks of companies and even some cryptocurrencies themselves act as a stock, however many are not regulated, even though the exchanges are liable, there is plenty of grey areas to get scammed in and research is your best bet.
Believe it or not, you can fork ( duplicate ) an exsisting cryptocurrency and customize that or you can develop one in many languages, there are plenty of resources to help you learn if you have the desire.