Can I still make a visa application to come to or stay in Australia?

Yes. The Department of Home Affairs is still accepting visa applications for all categories of visas.

There are some delays starting to happen and these can be expected to become longer over coming months. In fact processing for offshore applications may be put on hold. The Department of Home Affairs states:

As the Department focuses its efforts on managing the impact of COVID-19 on its critical services and employees, other non-critical services may not be delivered within expected timeframes. We apologise for the inconvenience and appreciate your patience during this period.

Medical checks and police clearances may be hard or impossible to obtain where these are required but the Department has advised that there is no need for concern about this and you will be given additional time to complete checks and provide the requested information .

If you are in Australia and have applied for a visa, you will be granted a bridging visa to allow you to stay here, pending the processing of that application.