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What are the minimum, maximum and optimal sizes of 1 input?
I don't believe there is any data yet for this: The general consensus is, however, that e.g. 10x1k is better than 1x10k.
What is the "stake split threshold"? Does this mean that when an input reaches a size of 2,000 or more coins - it is automatically split into 2 or more smaller ones?
Yes, the default is 2000 but you can change it yourself.
What is the annual ROI of POSmining?
For every block of 5 Vivid, 4 goes towards MN's and 1 goes towards people staking. There's one block every minute; the rest you will be able to figure out on your own depending on the timeframes that you had in pine.
What is the term of coinmature?
Are you asking what coinmature is or are you asking what the value of that is? 11 blocks I believe.
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I see that some of the MNs do not work well in the VIVID network and use old versions of the wallet. How can I ban them?
There's no need to ban them. If you really wanted to, you could manually do so using the setban command or using the console (GUI).