@Sterling Hiebert I have no idea why they wouldn’t show the contributions. As @Colleen F. mentioned, it would be best to call TD Ameritrade and ask them how much you contributed for each year. I would then explain to them what happened and have them help you recharacterize your contributions to IRA contributions.
The process for calculating earnings is laid out in IRS Publication 590a under Recharacterizations. https://www.irs.gov/publications/p590a#en_US_2019_publink1000230678
If you were making monthly contributions…you should technically do this calculation for each contribution.
There’s no tax and no penalty if you do this before you file your taxes. (other than the tax on earnings)
Good idea. I don't see why this couldn't be converted to a Roth via the Back-Door Contribution. Make sure that you don't have any other IRA money in existence, or it will be a taxable conversion. Make sure you follow the rules. :-) There's no reason to set up a separate Roth to do a backdoor Roth contribution though, you can just convert it to your Roth as usual.
I wouldn’t think you would run into any fees with this. I like Fidelity.
Final Note: This is a super complicated set of transactions so don’t feel bad if it gets messed up. And do not be surprised if you get a letter from the IRS in a year or so. It’s not a huge deal, just make sure you are following the rules and give them the additional information they need or correct anything that needs correcting. Feel free to reach out if you have any questions.
P.S. This is just a forum post, not tax, legal, or financial advice. You're not my client, and its not my fault if you screw it up, lol.