I use Tails OS with electrum. How can I mark or spend just these inputs?
If you enable the Coins tab, you can select (hold CTRL-key) all inputs you want to use. But: if you select dust transactions received on different addresses, you'll link them together compromising your privacy, which is the opposite of what you want.
My personal preference is to always use coin control, and choose my own inputs.
Is it possible with electrum? If not, is it possible to do on Tails OS with a different client?
Even if you could freeze certain inputs, you'd have to do this again each time you restart your LIVE OS. That's not a permanent solution.
Is this what's causing the dust transactions?
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If so, they may send you more dust after you make another (large) transaction, so consolidating the dust onto the real address won't help you.
Otherwise you could take all dust and larger inputs that belong to the same address, and send the full amount at once to a new (or even the same) address to consolidate inputs that belong to the same address.