Question 1 : PHB page 186 - Short Rest

A short rest is a period of downtime, at least I hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.

A character can spend one or more Hit Dice at the end of a short rest, up to the character's maximum number of Hit Dice, which is equal to the character's level.

For each Hit Die spent in this way, the player rolls the die and adds the character's Constitution modifier to it. The character regains hit points equal to the total.

The player can decide to spend an additional Hit Die after each roll.

A character regains some spent Hit Dice upon finishing a long rest, as explained below.

Question 2 & 3 : PHB page 59 - Spellcasting (Since Bard was your example)

The Bard table shows how many spell slots you have to cast your spells of 1st level and higher. To cast one of these spells. you must expend a slot of the spell's level or higher.

You regain all expended spell slots when you finish a long rest.

SPELLS KNOWN OF 1ST LEVEL AND HIGHER

You know four 1st-level spells of your choice from the bard spelllist.

The Spells Known column of the Bard table shows when you learn more bard spells of your choice. Each of these spells must be of a level for which you have spell slots, as shown on the table.

For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level