1. He is sitting at the computer.

2. He is working at the computer.
3. He is eating at the computer.
[Are they all grammatical? Is he doing the activities near or in front of the computer?]

Yes, all are grammatical. Yes, they all mean, whatever he is doing, he is in front of or near the computer.

From a grammatical standpoint, all of the sentences are correct. They follow the same structure of "subject + verb + preposition + object" and convey an action being performed by the subject.

In terms of the activities being done near or in front of the computer, we can infer different scenarios based on the prepositions used in each sentence:

1. "He is sitting at the computer."
In this case, it suggests that he is in close proximity to the computer and is likely using it or preparing to use it. It could imply that he is about to start working or engaging in some other activity on the computer.

2. "He is working at the computer."
This sentence implies that he is actively engaged in work while being in front of the computer. "Working at the computer" suggests that the primary action is happening directly involving the computer, such as typing, using software, or doing other computer-related tasks.

3. "He is eating at the computer."
This sentence indicates that he is having a meal while being near or in front of the computer. "Eating at the computer" implies that he might be multitasking, working while having a meal, or simply enjoying entertainment on the computer while eating.

Overall, the exact position of the person in relation to the computer is not explicitly stated, but these sentences suggest that the person is nearby or in front of the computer, engaged in different activities.