How can I tell if I'm making enough progress when working remotely? I am starting a PhD abroad, but due to the COVID-19 pandemic I cannot leave my country at the moment. My advisor has agreed that I can work remotely (starting later is not an option). While we can Skype and most of my work can be done online, I am concerned that having no access to the department, not being able to attend seminars/workshops, and not being able to meet/talk to other students in person will put me at a big disadvantage.

I am keen not to spend these initial few months slacking off and want to catch any problems before it is too late. However, I have always found it difficult to judge my own progress when studying alone, and with a PhD it seems that it will be especially hard as I need to learn a lot of skills in a new area. Also, because my advisor seems like a very 'nice' person who does not demand that his students work very hard, I am concerned that he will not tell me if I am underperforming.

Would it be appropriate to raise this with my advisor, asking him to tell me if I am not doing as well as his students usually do? Or are there any strategies for people working from home to judge if they are doing enough?
Yes, you should raise this issue, both with the advisor and with the university administration. Students need some feedback on their work and it is the university's responsibility to provide a way for that to happen. They need to provide the channels and you need to find a way to use them. 

But things are in a bit of chaos now, of course, and effective response can be slow to occur. 

Virtual seminars are possible using simple or sophisticated software. Perhaps you can set up (or the university can) a group of students and a professor or two willing to have an online session regularly. It isn't the same as face to face, but it can keep you engaged. 

But at a minimum, write a lot and note where you have problems. Ask a lot of questions, but make sure they are pretty focused. Share what you write with your advisor, by email or by posting it somewhere. 

Ask your advisor directly how you are doing and ask explicitly for next steps. You will most likely get suggestions about reading. Take a lot of notes on the readings and note things that puzzle you. Ask about them. 

If you are starting the research phase of the degree it is normally a fairly solitary effort in any case, but the advisor should be willing to review and respond to your efforts and your questions.