Ok, this might be unpopular, but I don't think that basing your decisions on fear is the smartest thing here.
*Frank is very secretive about his life. For example, I know he has a lot of money, but he won't tell me where it came from. He just told me it's not something I need to know. He also won't tell me any details about his current work. - Perhaps he needs to know he can trust you before he shares those details with you because of the nature of his work?
*They can't find any information about Frank on the internet, which they think is weird because his job would usually create a large digital footprint. - See above.
*Frank told his family about me and they don't like me already because of the country I'm originally from (he is defending me though) - His family's views are not his views. Cross that bridge should you get there.
*They think it's a bad sign we already had a few fights so early in the relationship (I did a few things that upset him which made him pout but I didn't realize it) - Fights? Or honesty. Were these instances where either of you were being unreasonable? Or perhaps you're both self-aware enough to be honest right from the start rather than putting up a front. And how these issues were handled will say a lot.
*They think he is controlling because he always wants to be on the phone with me and sometimes questions me or scolds me over decisions I make - Right now all you have is the phone. Is he requiring you to put aside other aspects of your life to be on the phone with him? If so, that's a red flag. If you are both just following the flow of mutual interest, it's totally natural to want to talk to each other, especially in the case of long distance where talking on the phone is really all you have. And SCOLDS you? Like in an abusive manner? Or does he question your decisions. Personally, I don't mind having some of my decisions questioned because I like seeing outside perspectives. Perhaps he is comfortable with that and perhaps your friends expect people to placate them and hide their opinions. This is something you need to ask yourself whether or not it crosses your personal boundaries.
*They also thinks it's weird that he messaged me in the first place since we are on opposite ends of the country, and he doesn't have any explanation for why he did. - Now this is just plain judgmental.
*They think he's moving way too fast (he already tagged me as in a relationship with him on facebook, and is discussing us moving together) - If you haven't discussed these things then yes, he may be jumping the gun. If its not something you are ready for, you should CERTAINLY address it.
*They see lots of similarities to my last failed relationship (started long distance with lots of early grand romantic gestures from him, turned out to be controlling) - I think they may be looking out for you because they know what you've been through.
*They think I just started dating again and shouldn't settle for somebody with so many red flags so quickly - The question is, are YOU ready? Do you feel ready? Do you feel like you know who you are, what you want, what you don't want, and what you expect from relationships?
Ultimately, I think if you agree with my comments above, I would say take things slow, listen to your gut, pay attention, but don't blow things out of proportion based on your previous experience. And trust that you learned a lot from your suffering. Your friends understandably want to protect you, but perhaps they are projecting their own fears on your current situation.
SO - take your time, ask questions, be honest about your feelings, don't be afraid to challenge and still remember to have fun.