Mining Pool Hub: how to understand if it is mining? I have just set up Mining Pool Hub, how can I understand if it is actually mining bitcoins (or other crypto-currencies)?

Because sometimes I see yellow alerts 
PoolApi  AHashPool has failed 
PoolApi NiceHash has failed

Also sometimes it appears "Status: Failed"

Could you explain, for beginner users, how to understand if the software is mining or not? And better, how to understand if the software it's mining at its best?

Right now this is what I see:
From your screenshot, I can see that you are using MultiPoolMiner. When you took the screenshot, MPM was busy running a few benchmarks in order to determine what algorithm is the best to mine with your hardware.

The Nicehash API probably failed due to the hack that they had in December 2017.

The software does not mine Bitcoin. It mines other currencies such as Ethereum, ZCash, Monero and a few others. In Mining Pool Hub, you have the option to setup auto exchange to a specific coin. Just log into MPH and look for "Auto Exchange" on the left hand side menu.

The simplest way to determine if the software is mining, is to have a look for another console window, and then scroll through that window to see if shares were submitted. You can also have a look in MPH at the "Balances" section in the left hand menu to see if you are getting balances in. For a more granular view, you can click on the currency in the balances view, that will take you to the currency pool, where you can view a dashboard with info.

How to understand if the software is mining at its best - it really comes down to how often you cash in and if you have the auto switch on. As the currencies fluctuate, you might get a less favorable exchange rate, so although you mined a coin that was most profitable a while ago, it might not be the case anymore. The best is to do your own research, and to monitor your miner. There are a few websites that can help you with crypto currency related info:

https://whattomine.com/

https://coinmarketcap.com/

You can also check on the Mining Pool Hub home page what currencies are more profitable.