The only real guidance we've seen for awarding inspiration is what you've seen in Basic, and there is a small bit of box text on it in the starter set adventure.
The Starter Set box text suggests awarding inspiration for when a character plays their flaws or their ideals in a way that is negative to them. This provides a small incentive for them to take less than optimal, but more interesting character routes.
As far as frequency, that is going to depend entirely on your game at this point. In general, I would be liberal with the awarding of it as a single die roll with advantage is not a huge mechanical advantage. However, you may want to meter it at least a little bit to encourage players to pass around the inspiration football.
There are guidelines for creating playable races in page 285 of the DMG, however, it doesn't go into detail on creating Large races, specifically (nor do they really go into detail on making medium characters, mechanically, save for the 'compare to other already-established races' approach). This is largely because playable races are only sized between Small and Medium (4 to 8 feet tall).
Take a look at the Goliath in the Temple of Elemental Evil player's companion, the Minotaur and Centaur race in their Unearthed Arcana version, and the final version of Minotaurs and Centaur in Guildmasters' Guide to Ravnica, all these races sound like they should be Large. In fact, if you take a look at page 223 of the Monster Manual, you'll find that Minotaurs are Large creatures, despite this, playable minotaurs are Medium. Of course, you could argue that the Krynn minotaurs who don't dwell mazes have evolved to be smaller. Then again, who's to say it wasn't a design constraint? ;)
So, why aren't there Large player-characters?
Weapon damage dice
In page 278 of the DMG, you can see rules on damage dice of creatures. A Large creature is going to wield oversized weapons, this means their damage dice are doubled, tripled for Huge, and quadrupled for Gigantic. A Large PC with a Glaive will be dealing 2d10+str, almost doubling the damage output just by being large, at 1st-level.
Area
A Large creature occupies a 10x10 ft area, making it more of a threat in battle especially when it comes to blocking and generally being a 'presence' in any encounter.
Aura Areas
As mentioned in this tweet by @ThinkingDM, auras emanating from Large PCs cover more squares than Medium PCs. Specifically, for a 5' aura, Large PCs cover 12 squares versus the Medium's 8 squares. In 10' auras, Large PCs cover 32 squares versus the 24 from Medium.
Squeezing
In order to accompany any typical adventuring party, a Large PC will need to squeeze in most places a typical adventuring party would visit. Whether it's a tavern, a forest gnome's tree house, or a mine tunnel made for dwarven miners, a Large PC will be continuously at a disadvantage while squeezing through most other terrain a Medium creature would have no problem fitting in.
These traits, inherent in the creature's size alone, make a Large creature fairly overpowered in most any game.
Best Answer
First, there are no lists of punishments in the rules.
Second, the default D&D 5e setting is a fantasy medieval one, as such, imprisonment is an inappropriate punishment. Imprisonment as a punishment is a late modern development from the early 19th century:
A more appropriate punishment might be the pillory or stocks both of which were used to restrain the criminal in a painful position (Exhaustion might be an appropriated D&D mechanical outcome) and to allow the populace to humiliate them by laughing, hurling insults, rotten vegetables, offal and, of course, human or animal excrement.
Here is an interesting list of historical punishments for both criminals and children from around the world. I give thanks every day I was not an Aztec child.
This presuposes that the rule of law is suficiently established that a common assault is a matter for local law enforcement. In medieval times (and some places today) retribution was a private matter. For example, gathering a bunch of friends together and beating the snot out of the perpetrator.