No you can't buy EC like that. Sites that sell it are known as goldsellers in most MMOs. Never buy from them, just make your EC in game.
The game shouldn't crash when you alt tab out, and doesn't for most people. You can try general stuff like making sure your drivers are up to date, or running it in Windowless Fullscreen mode. Beyond that, we'd need more information about your system and setup, and it would be better posted in the Technical Issues forum.
Foundry Missions: 1) The Source of Power (ST-HSWUBD5TQ) [Federation] 16+ -----=====*****<[ Fleet Recruitment Thread ]>*****=====-----
Purchasing EC from a third-party seller runs the same risk as buying from any goldseller - the high probability that the process will install malware on your computer, often in the nature of keyloggers (the better to capture your bank login information).
It's not hard to get ridiculous amounts of EC just from selling things in the Exchange, and recycling anything you can't sell through the replicator.
"Only a fool fights in a burning house." - Commander Kang, "Day of the Dove"
Something to know about goldsellers: The whole sweatshop currency farming thing died years ago, it was too labor intensive to be profitable in most games.
They get the currency they sell now by using keyloggers to compromise accounts - often of their own customers, but their primary means are distributing fake hacks, cheats, or bots on different websites that are actually keyloggers and using malicious scripts attached to their advertisements to install keyloggers on people using out of date versions of Internet Explorer.
Even if you take computer security seriously and are successful in buying EC without having your account stolen, you're still taking something that was stolen from another account.
To help avoid crashes, switching form fullscreen to windowed mode can help. It's usually not the game, but other software not relinquishing its control of resources that causes full screen games to crash or lock on alt+tab.