The "Hand" is the set of accessible cards that are available to the player at any given point during a match.
The cards of your hand are visible to you at the bottom of the battlefield. The cards of your opponent are hidden from you at the top of the battlefield.
How it works
At the beginning of the battle you select your starting hand, this is called the Mulligan. The player who starts the battle starts with 4 cards in the hand, the other player starts with 5 cards.
During the battle, you use cards from your hand (e.g. deploy units, issue orders, perform countermeasures) and draw fresh cards from your deck.
Orders, Countermeasures, or effects on certain units can impact your hand (e.g. you might be forced to discard cards or you might draw some extra cards).
The cards in your hand that you can afford to play are subtly indicated by a yellow credit cost marker (yellow text on black), otherwise the credit cost marker is a grey number on black.
Full hand
You can only have up to 9 cards in your hand. If you already have a full hand with 9 cards, then any extra cards you draw will be automatically discarded.
Empty deck
You can only draw new cards from your deck as long as it is not empty. Once your deck is empty, you cannot draw cards from it. Whenever you attempt to draw from an empty deck (e.g. at the start of your turn) your HQ takes 1 damage. For each subsequent start-of-turn draw, the damage your HQ takes will increase by 1.
Nowhere can I find an explanation of what the numbers on the shields mean (at the bottom of the cards). I guess it's something to do with attack and defense strengths, but there really should be a proper and detailed explanation somewhere, along with an explanation of what the results of an attack will be, based on those numbers.
Those numbers represent the offensive and defensive strength. For a more detailed explanation of the card, please check out this article: https://kards.zendesk.com/hc/en-us/articles/360026768151-Cards
If you refer to the Heavy Armor 1 ability, please have a look here (Heavy Armor 2 works similar) : https://kards.zendesk.com/hc/en-us/articles/360026532571-Unit-ability-Heavy-Armor-1
For those cards i rejected in mulligan, do they return to my deck pool or are they discarded for good?
Cards rejected in Mulligan are shuffled back into your deck. You can draw them later then.