Does anyone know if trips to places like Monchique/Silves are still run in January or are there other means of getting here in this month?

You can get a bus from Portimao. Possibly from Lagoa as well. I've not done it but checked last week for future reference. The buses tend to turn off the main routes and whilst this makes for a longer journey, you do get to see some interesting places. A lot cheaper as well.

The regular tour companies like Mega etc. run sightseeing tours to all the usually places in January as well. Heini