First off, well done for installing something like this. External insulation is a good way to go.
This isn't going to be easy. Well, put it this way, the fixing should be easy, but the potential for making a mess of the cladding is rather high.
Sleeve Anchors - no problem with "head" size. Use anchors with a "hex" (spanner) type head.
I would suggest at least 150mm long. That would give a grip length of about 60mm. Given a decent, smooth hole, that should be enough.
The trouble is, after you've drilled the hole, there's no way of inspecting it to see if there's any crumbling or whatever. Maybe even go as far as using 200mm anchors. A 200mm could be used to fix a 100mm thickness to masonry, so it would make more sense here.
You'd need a drill bit of at least 250mm length. This would ensure the drill finds its way through the whole thickness of the brick.
Sleeve anchors can have M12 heads (12mm diameter bolt. ) Depending on your bracket holes, M10 may be enough.
It's going to take care for a clean job. However, your bracket has several holes, so no matter if one or two don't grip properly. Any one of these would be more than capable of holding a dish bracket.
Or................ maybe better still, self-tappers...................
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