[Mondial]

Yes the safety rated Y cap should be fine in both locations. Its not really needed across the transformer for safety but they are usually rated for 240VAC so its a good choice.

I would go with a 2.5A slo blo fuse, or maybe even a 2A if your measured draw is less than that. Its better that the fuse blows before anything else expensive. In any case the fuse is easy to replace and if you find it blows under normal operating conditions you can up the rating slightly.