Yes, you can gape (or gawk or beam) at something, or just gape/gawk/beam in general.

For gaping or gawking, usually if you don't specify the subject, it's understood from the context, though you can just beam in general without aiming it at anything particular, in which case you're just describing having a huge smile.

Example:

"I'm going into the forest tonight," Harry said.

Ron gaped. "The forest? At night? Are you mad?"

Since it's a conversation between Harry and Ron, it's implied that Ron is gaping at Harry, even though it isn't stated.

Yes, you can gape (or gawk or beam) at something, or just gape/gawk/beam in general.

For gaping or gawking, usually if you don't specify the subject, it's understood from the context, though you can just beam in general without aiming it at anything particular, in which case you're just describing having a huge smile. ("Sarah bounced into the room, beaming.")

Example:

"I'm going into the forest tonight," Harry said.

Ron gaped. "The forest? At night? Are you mad?"

Since it's a conversation between Harry and Ron, it's implied that Ron is gaping at Harry, even though it isn't stated.