I. It's written that gate bursts can't create monster surge. But it's written in the paragraph about sealed locations. On the other hand there cannot be open gate on such locations (I guess moving gates from LatT can't move to sealed ones). So can the gate burst create monster surge at any circumstances?
A gate burst only happens when there is a seal - which means that there isn't already a gate at that location. A gate burst can only happen when there is already an open gate. So a gate burst and a monster surge can never happen at the same time as they are tripped by two opposite effects.
Now if you mean can Mythos cards with Red backgrounds on the gate cause a Monster surge if that gate is already open: then the answer is yes. But this isn't technically a "burst" it is just a card that would cause a burst if the conditions were right.
II. Returning to Arkham during Mythos phase. Sometimes it happens. Does it mean that investigator can try to close the gate during this turn or he has to wait for the next Arkham Encounters phase (it means that any monster present at this location will have to be evaded/defeated before).
Next turn. Closing happens only during Phase 3. If Phase 5 is what sent you back, then you must wait for the next Phase 3.
The exception would be if the Mythos card specifically gave you permission to close the gate.
III. What about the Dunwich Horror track while Dunwich Horror monster marker is present on the board. Does it fill up and generate terror? And what happens when DH is killed? Do DH track resets or it's stays on whatever position it was?
No, the track is completely ignored while the Horror is out. It only starts over once the Horror is gone. Once the Horror is "killed" you start tracking again from the beginning and he can come out again once the 3rd token is placed.