Is there a way to apply a default label of my choosing to all incoming Gmail messages?

Question

That is, the label of my choosing should be applied to all incoming emails notwithstanding the sender/recipient/subject/etc.

If possible, can the above be taken further wherein the label is applied only if it is destined for the inbox?

i.e. the email is NOT affected by a filter that "skip[s] the inbox".

Answer 1

The search from:* will match any incoming message. A filter with that that applies a label should do what you want. (It seems to work just fine in my tests.)

Matches: from:(*)
Do this: Apply label "default"