Ultimate Authority
Ultimately, the decision on appropriateness when writing CCC adventures is determined by the DDAL administration. Each Convention Created Content module must be submitted to them for approval before it can be played. Groups and individuals with a long track record of producing quality content are given more leeway.
Established Patterns
It works out very simply...
- Tier 1 = Uncommon
- Tier 2 = Rare
- Tier 3 = Very Rare
- Tier 4 = Legendary, but not all that often.
A variety of common magic items are a fairly recent occurence. To my knowledge, they have not been explicitly included in anything except DDIA-XGE: Underworld Speculation, the introductory module for Xanathar's Guide to Everything where they first appeared.
How many? One
As for how many magic items: one, always one - regardless of length. Hour-long introduction modules have none, and Epics sometimes have more, but neither are part of the CCC program.
I can speak from personal experience with the CCC program. I am indirectly affiliated with a CCC writing group; they submitted a module for a convention I staff for. It had two magic item rewards, both very thematic. They were told to pick one or the other by the DDAL administration.
A Note on Precision of Language
The question says...
the process for submitting adventures from conventions to Adventurers League to become certified “legal” CCC-AL adventures.
...but it's not an accurate statement.
CCC adventures are sponsored by and affiliated with a convention they premiere at, but the creation process starts long before the convention takes place. They're not created freely by the conventions to "become certified" later. They are authorized by the DDAL administration to premier at a particular convention before writing even truly begins.
Yes, bugbear is a legal AL race
According to the D&D Adventurers League Players Guide (v 7.0) page 2:
All of the races and classes presented in the Player’s Handbook plus
one other resource from those listed below are available to build your
character (PHB+1).
[...]
- Volo’s Guide to Monsters (VGM)
The only restrictions are:
Races that grant flight at 1st level, and options
presented in other resources—such as the Death
Domain found in the Dungeon Master's Guide (DMG),
or content from the various Unearthed Arcana
articles—aren’t allowed for play unless you possess
specific campaign documentation that indicates
otherwise.
Since bugbear is a race presented in Volo's Guide to Monsters and one that does not grant flight, it is allowed per AL rules.
Bugbear was even mentioned officially as an allowed race in
Volo's Guide to Monsters: An Official Reference for D&D Adventurers League. They retired the document when they dropped the restriction on which race could join which faction (discussed in the faction section below). As a result the document is no longer available.
Note that you are required to have access to a copy of Volo's Guide to Monsters (physically or digitally) in order to use this race. You can find the race here on dndbeyond. If you desired, you can purchase just the race from dndbeyond instead of the whole book.
Quick note about factions
I know you didn't ask, but just in case there is any confusion, in July 2018 they removed a rule in which certain monstrous races were required to join certain factions. Now, they can join any faction they want per the new “any race; any faction” mentality.
Best Answer
Unearthed Arcana articles
The content of the Unearthed Arcana are designed partially for play-testing ideas and seeing where the fans are focused in class, race, and option design. They are all optional content that is designed for WOTC to perform surveys on, improve, and refine before a possible release either as a later form of Unearthed Arcana, or in books to be later sold. An Eberron source book has been hinted at by the direction of the First Unearthed Arcana entry and other information, but they are very vague hints and nothing concrete about their plans are known yet.
Adventurer's League characters
The documentation for the Adventurer's League is very specific about what content can be included in the character creation process, and for many reasons. Even within larger bodies of contents, such as the Elemental Evil Player's Guide, individual options may not be available to players. The Aaracockra is an example of this. Every season will have its own options available to players. These options will always include the Player's Handbook, and will generally include a Player's Guide for the season if one has been printed. Even class options from the Dungeon Master's Guide are generally not allowed (with very limited exceptions based on certs offered at conventions).
What this means
The bad thing about this is that no characters outside those that are discussed in the Adventure League Player's Guide is available for play in the Adventure League, and even within the sources that it allows you to use, you are restricted on combining options. It's not so much about unofficial versus official, as what they are allowing in an organized setting specifically.
As an example of restrictions placed, the Sword Coast Adventurer's Guide is allowable for all story lines, but can not be used in conjunction with the Elemental Evil Player's Guide, even if the character is from the Elemental Evil story arc.
Currently there are no Unearthed Arcana entries even mentioned in the AL Player's Guide, so you cannot use the options presented within any of them. It is highly unlikely that any Unearthed Arcana entries will ever be present in AL, since they are considered to be in draft form. When the options are refined (assuming they are not scrapped), they will become available through official releases such as the Elemental Evil Player's Guide and the Sword Coast Adventurer's Guide.