Would a player casting Detect Magic make him aware of the spell and spellcaster?
The caster of Detect Magic would be aware of a magical effect nearby for Clairvoyance and Scrying, but would be unable to locate it or discover its school of magic. They would be unaware of Locate Creature. In each case they would be unaware of the spellcaster.
The relevant portion of Detect Magic states (emphasis mine):
For the duration, sense the presence of magic within 30 ft of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object [...].
Parsing this, we can see that Detect Magic gives you an additional "magic sense". This sense is unrestricted in terms of visible or invisible creatures/objects.
It also gives you the ability to interrogate the properties of the magic that has been placed on visible creatures or objects. This additional interrogation is specifically limited to those that are visible.
For the specific spells in question we need to look at their text to see how they interact with this new sense you have gained.
Clairvoyance and Scrying both create an:
[...] invisible sensor [...]
which you would be able to sense but not interrogate further (as it is invisible - unless you can see it through Truesight for example).
Locate Creature however does not create anything for you to be able to detect in your vicinity, so your new sense will not make you aware of it.