Blockchain.info has APIs to generate and resolve firstbits.
Reusing an address is a security issue if you have a weak random number generator, as was an issue with the Android Bitcoin Wallet. I should note this was android's fault for using a bad generator and was fixed quickly by the app developer, though some people lost coins because they had signed multiple messages (i.e. transactions) with the same address and ...
For a start and to get to know the different exchanges and wallets you should checkout: https://www.bestbitcoinexchange.io/ (I'm not affiliated with that website).
To buy and sell Bitcoin I recommend https://gemini.com and https://xcoins.io. https://coinbase.com is popular but I'm not a huge fan of them for a number of reasons.
Just sign up and add your ...
Having seen that yes blockchain.info no longer offers this service I was able to find only one other Block explorer that do offer the FirstBit lookup on addresses:
Hope this helps :)