push button on toilet cistern faulty?

Yes

In cistern On the top of flush sistem are attached 2 long plastic screws next to each other, one is for big flush and next for smal flush. Also you can them screw in or more out and this way is possible manage how big will be content of flush . Some times happen that's crew isn't on right position, losted in cistern or demaged so than flush button doesn't work. This problem can be resolved with similar type of screw, plastic or metal one which is also most of time necessary little bit remodeled the screw to get same shape as original is . If is demaged little bit silver top push button also is possible repair this problem but that's dependent how big is demage, for example if is demaged more as 20 % off the button bodie than I recommend to replace it with new one .

It could just need adjustments on the adjustable rods

Yes it can what brand is cistern

Not better new one

Push buttons are fairly easy to be replaced and can rarely be fixed. For the coat of trying to fix it won’t cost much more to just replace unless it’s the siphon that’s causing the fault

Yes it can be but its eaiser to replace the mechanisim.

Yes, very easily with a replacement part.

Some of them can be, but it would be easier just to replace with a new one. The cost probably would be same

That depends what is needed. Sometimes they stick and may just need a little lube, or the hole may not have been cut wide enough and it just needs groves cutting for the pets to move smoothly. Otherwise, you may be able to just get a replacement button.

Hope this helps.

Most probably needs replacing