New concrete over old slab

Ideally you would take the slab out and have a look at the base underneath as it would be more likelihood the base has moved in order for the concrete to break or possibly the concrete was not installed correctly but yes you can install over an existing slab but would recommend bonding agents to make sure they adhere to each other and would recommend reinforcement mesh to help stop cracking in the future

I would break out the old base as there is likely a reason it has moved/cracked in first place. Eg poor / lack of sub base. To save on costs you can use this hardcore as part of your new compacted sub base and new concrete on top of that. If just couple bikes and mower then mesh won’t be needed long as mix and lay it well off course, but if large and heavy items inside then it’s best to add it to prevent cracking.

It is not normal practice to do that, as can cause heave. You need to seal the existing slab and then I would do the rebar but for it to be any use it needs to be at 300mm centres as otherwise you just bonding a small bit. I would rough up the existing personally, to form a rough coat then seal it then pour new concrete.