Ok, a few things here.
Do you have any antivirus software installed that could be preventing the game from importing these maps correctly? Please check to make sure this isn't the case.
Are you running osu! as an administrator? If not, does it work if you do?
Check to see whether or not you have FIPS enabled. If it is enabled, try disabling it. This seems to be a common cause of beatmaps not importing correctly for whatever reason. It also causes the updater to fail too sometimes (not sure how yours would have randomly started working again though). This also usually shows in your runtime.log, which yours didn't, but it won't hurt to check.
To do this, go to Control Panel > Network and Sharing Center > Click on the item listed in connections > Click on the first properties button > Security Tab > Advanced Settings > and
uncheck the box in that window, it should say "Enable Federal Processing Standards (FIPS) compliance for this network"
Also go to: Control Panel > Administrative Tools > Local Security Policy > Expand Computer Configuration > Windows Settings > Security Settings > click Security Options > Look for "System cryptography: Use FIPS compliant algorithms for encryption, hashing, and signing" and double click on it, hit disable, and apply.
You can also probably google something like "Disable FIPS Mode" to find more detailed versions of what I just wrote.
This happened to be the first link that came up when I Googled that and there is a more detailed section on how to make sure it is disabled at the bottom. I also found
this, which could be helpful.