Can a neutral be shared beween the line and load side of a GFCI if it's on the same circuit?
This is a common issue that arises from the previous meaning of the word LOAD.  

You're used to talking about the cables in a box as "Line" meaning the supply cable from the service panel, and "Load" referring to the cable(s) that go onward to other points-of-use.  

With GFCI, you have to throw that definition out.  In fact, I use the word "Onward" to refer to those onward cable(s).  

GFCI has hijacked the word "LOAD" to mean extending GFCI protection to also protect certain specific onward outlets or points-of-use. You should never, ever use the LOAD terminals on a GFCI unless you mean to do precisely that. 

Usually people go after the LOAD terminals merely because their old receptacle had wires on 4 screws and they don't know where else to put the extra 2 wires.  This results in protecting downline loads inadvertently - they have no idea what effect that has, and have no idea how to fix it when it starts tripping.  Don't do that.  

When you actually, really do want to protect a downline, you must take that particular downline's hot and neutral wires both, and put both of them on LOAD.  You would never put just one on LOAD. 

So you say you have a kitchen circuit that feeds aquarium, gas stove, vent and fridge.  Let's go through those loads. 


Aquarium - oh yes, you want that on GFCI! 
Gas stove - Is it grounded? A steel box that is grounded is vanishingly unlikely to have the kind of problem GFCIs help with.  It might be a source of nuisance trips though. 
Vent - is hardwired and does not need to be on GFCI. Again if grounded, GFCI is of little use here. 
Refrigerator -- is a human-safety nightmare for GFCI.  It's a steel box, grounded, all the mains electric is in the bottom back where it's totally inaccessable, and you're really not likely to drop it in the sink.   So it's simply not a use case for GFCI at all. GFCI does not help fridges. However, a GFCI nuisance trip can take out a fridge, and now you have a huge human safety problem in food spoilage.  Fridges do not need to be on GFCI. Further, fridges are notorious for tripping GFCIs themselves.  Putting this on GFCI is a bad idea. 


But if you have any other loads, evaluate them on a case by case basis and decide whether to attach their hot + neutral to GFCI LINE or LOAD.