My account got approved! 8)
I also have my investment accounts with Fidelity, an individual and an IRA. I only use the phone app for trading and only use the desktop site when I have to.
Aside: message like good faith violations, etc, only show up on the desktop site and not in the app. I made a rookie mistake and triggered a 90-day settled-cash-only trade restriction due to multiple good faith violations in short order, but I didn't find out until it was too late because I never logged into the desktop site. No more jumping back and forth between preferred series for a while for me.... :(
I tried to buy some FNMAH on the app a few months ago and got a message saying that that symbol wasn't available to buy, limited to closing trades only or some such. After a call to the Fidelity rep I found out why: they don't let anyone (even then-President Obama to quote the rep) buy variable-rate preferreds. So if you're trying to buy FNMAS, FNMAH, FMCKJ, etc. hopefully this explains why you're having trouble.
I own some commons but mostly preferreds. I started in the low yielders because they were trading at the biggest discount to par: FNMAL, FNMAG, FNMAN. A few weeks ago I started to migrate to the mid yielders: FMCKL, FMCKO, and last week I added on some FNMAJ. I now have about 20% low yielders, 60% mid, 20% FNMAJ.
I downloaded historical price data from NASDAQ's website and ran a linear regression using dividend yield as the explanatory variable and the average percentage of par each series traded at between Feb 20, 2008 and Jun 30, 2008 as the dependent variable. I got
(% of par) = 25.65 + 9.284 * (div yield)
where div yield is in percentage points (i.e. 7.625 for FNMAJ, not 0.07625). The r^2 value was 0.922. According to this, at least as of a few weeks ago, FNMAJ and FMCKL were the best bargains while FNMAL and FNMAT were the worst.
I also ran a linear regression using div yield to explain average % of par for Dec 2016 and got r^2 = 0.9240. This tells me that the market seems to mostly assume that dividends will get turned back on rather than entire series of shares being redeemed at par. That's the main reason I started switching out of the low yielders.