Sims aren't unlimited, you just keep getting more as you level.
The shard drop rate from cantina can be quite low most of the time, but other times you might get a lot. You don't get more drops one way or the other.
You sell the mining droids, they have no other use.
It might just be me, but I seem to have better luck getting shards in the Cantina doing a 7 or 10 second count between pushing the Sim button rather than just pushing it over and over.
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The shard drop rate from cantina can be quite low most of the time, but other times you might get a lot. You don't get more drops one way or the other.
You sell the mining droids, they have no other use.