Fell for a pop-up alert scam. Now what?

The thing I'm worried about is 1) if they downloaded anything bad on my computer 2) if they can use my information to take more money from me.

Yes to both questions. Read Phony "tech support" / "ransomware" popups and web pages.

You may be the victim of a crime, perhaps a felony offense, but for all you or anyone knows the criminals may be well beyond the reach of your jurisdiction's law enforcement resources.

Your actions at this point can range from doing nothing at all, to erasing the Mac and reconfiguring it. Separately, it would be prudent to assume the intruder has gained sufficient information from it to effectively commit identity theft. Computer tampering and identity theft are legal matters that go well beyond the scope of this support site, and for which you should seek appropriate legal counsel. Therefore I can only offer technical guidance regarding your Mac itself, which may be considered evidence in a criminal proceeding that only you can decide to take upon receiving that counsel.

It's very likely that these scam artists are looking for nothing more than a quick buck, which they got, but it would be irresponsible for me or anyone to tell you there is nothing else to worry about. Without an in-depth, hands-on inspection of your Mac, the absence of some nefarious exploit cannot possibly be confirmed by anyone or anything. Even an exhaustive personal inspection by uniquely qualified experts would leave an element of doubt. For those reasons, at a minimum it should be immediately disconnected from the Internet (unplug its Ethernet cable and turn Wi-Fi "off") after which you can decide whether to preserve it in its present condition as evidence, or its contents completely erased, permanently removing that evidence. Decide how you want to proceed and write back.

.... what safety measures can I take to fix this and prevent further problems?

There is nothing you can do to prevent the appearance of phony popups, any more than you can prevent some uninvited stranger from knocking on your door or calling your phone, trying to sell you some garbage you do not want or need. Same scam, new era.

I realize I'm not getting my money back.

Actually, you might. You should report this event to your credit card company (assuming that's how you paid). Credit card companies have no tolerance for fraud.

For additional actions to consider, read the following:

http://www.consumer.ftc.gov/articles/0346-tech-support-scams

and

http://www.ic3.gov/default.aspx

You should erase and reformat your hard drive, then restore your computer from a backup made prior to when you allowed them access. Change your passwords and other critical information also. You don't know what software might have been installed. If you paid them by credit card, contact the credit card company, and close out the credit card.

You are welcome.