ASICs are basically special computers created to do only one job, contrary to normal computers, which are made for general purpose. This characteristic makes ASICs very efficient for @mining.
As long as the encrypted output amounts you create is equal to the sum of the inputs that are being spent (which include an output for the recipient and a change output back to yourself and the unencrypted transaction fee), then you have a legitimate transaction and know no Monero is being created out of thin air. Pedersen commitments mean that the sums can be verified as being equal, but the Monero value of each of the sums and the Monero value of the inputs and outputs individually are undeterminable.
As stewards of the project, the Core Team manages and maintains infrastructure where centralization cannot be avoided (domains, website, github repositories...). Its members act as mediators as they see fit and aim to weigh consensus in the community, perpetuating the quality interactions that made Monero the successful project it is today. The Core Team does not and has never received any financial compensation.
As the name suggests, the Monero Research Lab is the workgroup focused on Monero-related research. It's formed by scientists finding ways to improve Monero's protocol and features. Most of the protocol improvements that make Monero amazing, like CLSAG and @Bulletproofs, are the result of the efforts of this workgroup.
As you can see from the picture above, every account has an index number that you can use to switch from one account to the other using the command `account switch [index]`. For example, using the picture above as reference, if you would like to switch to the 'Donations' account to monitor it, you can do so by giving your CLI this command `account switch 1`. Now you are sitting on your 'Donations' account and you can start using it right away.