The best areas to look for will be Nicholson Street, Newington and Marchmont. I would suggest websites like zoopla.co.uk or even https://www.gumtree.com/ . There are a lot of Facebook groups for stuff like this.
IS should pick up if it's down for people outside the network (the uptime thingy on the alerts page is off-site). If you continue to have problems, you could ask via Unidesk and they should be able to help.
There's also books you could read as an alternative or precursor to therapy. They contain a lot of methods, worksheets, and tips for managing these conditions. For depression, consider: https://www.amazon.com/Feeling-Good-New-Mood-Therapy/dp/0380731762/ref=sr_1_3?dchild=1&keywords=feeling+good&qid=1606896623&sr=8-3