In my experience just pointing a smartphone camera or other small-lens digital camera down the eyepiece yields pictures of quite acceptable quality for documenting observations (in my case mostly of mosses and lichens), no need for an advanced camera setup
Many insects require genitalia dissection or close analysis of hairs to identify to species, a dissecting microscope is used for those kinds of things.
Moss sometimes require microscopic views of cells and fungi often require microscopic views of spores for identification, which you’d use a compound microscope for.
The last common application I can think of is that you can get samples of water from any natural environment and find microscopic organisms in it (zooplankton and phytoplankton etc.). Depending on the scale of what you want to look at you could use a Petri dish in a dissecting scope or depression/well slides in a compound scope. Also moss, lichen, honestly really any natural surface will have microscopic organisms on it especially if it’s damp.
This replaces the eyepiece on a telescope or microscope which should be one of several standard sizes. These are commonly available in 1.25" to 2" sizes (for telescopes) and 23.5 mm (0.965") for other devices (there may be other sizes available or that have adapters for other sizes), with mounts for various cameras like Nikon, Canon, Olympus, Sony, Minolta &c. It is important you match the size of the eyepiece precisely as well as the correct mount for your camera. These are inexpensive and most can be had from ‘Amazon’ for less than $30 (Search = “t mount for microscopes”). Note that for this the camera lens must be removable.
Alternatively there are USB cameras available which again replace the eyepiece. One brand comes with adapters for 23.2, 30, and 30.5 mm (Search = “USB camera for microscope”). These are worth considerably more but should be available for less than $100.
For me the most obvious use case is for aquatic studies. This is my cyanobacteria observation, provisionally identified as Oscillatoria:
The was with a USB microscope, so no slide. The wider of the two black lines is 200 micrometers thick. I believe that compound microscopes (which I’m guessing is what you mean by a “professional” microscope) can get better magnification than this.
One useful thing you can do with a microscope (although it might take some practice) is photographing spores from mushrooms. Sometimes it’s the only way you can tell two similar species apart (besides DNA sequencing).
Yes, this will work - our students are getting quite proficient with it. I see some are no longer looking into the microscope at all, just pointing their phones at the eye piece and then looking at the slides and labeling them on their phone screen.
I took some photos using an inexpensive digital microscope (which I have slightly modified to improve photo quality) of some very small creatures in the vernal pools, as well as some algae. I was going to upload them to the microscope project but, after reviewing their rules, decided they only wanted observations of items which are essentially invisible to the naked eye. IMHO, the microscope project should be renamed to the microorganism project and the microscope project should become more inclusive, or are my interpretation of the microscope projects rules incorrect?