If the spell requires you to see a creature to target then you can't target yourself when you are invisible. The exception to this is if either:
- The spell/effect that caused the invisibility allows you to see yourself
- You have some other item or effect (like Truesight) that allows you to see invisible creatures
Supporting unofficial tweet from Jeremy Crawford:
You can't see yourself while invisible, unless you're under the effect of a game feature that says you can.
If you are blinded you can't see, and as a result you can't use spells that require you to see the target as you can't see anything
BLINDED
- A blinded creature can't see and automatically fails
any ability check that requires sight.
- Attack rolls against the creature have advantage, and
the creature's attack rolls have disadvantage.
Here are some additional unofficial supporting tweets from Jeremy Crawford: here and here
Yes, the sensor can be seen with truesight
I will briefly state what has already been pointed out in Dinomaster's answer:
The clairvoyance spell specifies that it creates "an invisible sensor", and truesight it described as allowing a creature to "see invisible creatures and objects", so this implies that such a sensor can be seen via truesight, although since a sensor isn't explicitly described as an object, it's not conclusive evidence...
In addition to that, a similar situation exists for the spell scrying (PHB, pg. 273), which is made more explicit:
... the spell creates an invisible sensor within 10 feet of the target. [...] A creature that can see invisible objects sees the sensor as a luminous object about the size of your fist.
So not only can creatures with truesight (or any creature that can see invisible objects for any other reason) see the sensor, but according to scrying, it looks like "a luminous objects about the size of your fist".
Given that the language regarding the "invisible sensor" is the same in both spells, it seems as though invisible sensors can be seen by creatures with truesight, and furthermore it's likely that the appearance of the sensor described by scrying would be the same for clairvoyance as well (or at the very least it gives the DM a precedent to follow).
Best Answer
No.
The invisibility spell's description states:
No part of the spell's description makes an exception for the subject of the spell's sight. On the contrary, the spell's description goes out of its way to clarify that the caster can't see creatures that they make invisible using the spell unless they have the ability to see invisible stuff. (The spell does contain the line "If you cast the spell on someone else, neither you nor your allies can see the subject," but that doesn't automatically mean that if you don't cast the spell on someone else, you can see the subject.) The spell doesn't even allow a saving throw to disbelieve the illusion.
Moreover, the invisibility spell is part of the glamer subschool - and unlike some other subschools of illusion, glamers aren't mind-affecting, don't only affect certain creatures, and explicitly change the sensory qualities of the things they affect.
Nearly every effect in the game that renders something invisible references the invisibility spell, meaning that all other sources of invisibility are subject to this same limitation. (As kindly pointed out by Peregrin Took, one known exception is invisibility sphere, which explicitly states that those affected by the spell can see each other and themselves - a line conspicuously absent from invisibility.)