Question 1: Could it be possible to use present continuous instead of "will be working"? "He is sure that he is working for them next year."
Some other languages may allow you to add "tomorrow" or "yesterday" to the present tense, and the result is understood. Even in English, there may be certain cases of that... However, typically in English you ought to properly conjugate the verb. Use the past tense for the past, and the future tense for the future.
Examining this sentence "He is sure that he is working for them next year." it does not sound right. The tense is wrong.
Question 2: Can you use "going to work", as in "He is sure that he is going to work for them next year."
Yes. "going to" is future tense.
Note: If he worked for them last year, and he is going to work for them next year, then the original wording "as well" should remain. "He's sure that he is going to work for them next year as well." Otherwise, it is slightly confusing, because the listener thinks "He is going to ... but wasn't he already working for them?"
Question 3: what's the meaning of this sentence with respect to the original?
They are very similar. Nearly interchangeable.
"will be working" is future continuous. From https://www.ef.edu/english-resources/english-grammar/future-continuous/
The future continuous refers to an unfinished action or event that will be in progress at a time later than now.
"going to work" is also a future tense. From https://www.ef.edu/english-resources/english-grammar/future-going/
The use of going to refer to future events suggests a very strong association with the present. The time is not important, it is later than now, but the attitude is that the event depends on something in the present situation that we know about. Going is mainly used to refer to our plans and intentions or to make predictions based on present evidence.