[@Darkmoon Angel] The region doesn't have a name. Your trainer gets TP with every post, and your Pokemon gets a single level for a battle with wild Pokemon every fifteen days. CP is counted by every post as well, but applies to you rather than to your trainer. And yes, you're allowed to catch any type of pokemon in the village, as long as it fits with your rank/device (Pokeballs can only catch basic Pokemon). 

Battles, especially informal ones, currently play out with a lot of freedom. 

[hider=Battles][hr][color=fff79a]   How to Battle:   [/color][hr][indent]
Battling is a long time tradition in the Pokemon world, but to make it work in this play-by-post setting, some changes had to be made. Moves should be moves that the Pokemon are actually capable of carrying out, most likely pulled from their moveset (reference Bulbapedia for movesets, if needed), as TMs have not yet been incorporated. There are two different options for battling:

[indent]Battles: Friendly VS. Competitive VS. League: Friendly battles are done just for fun; there is nothing to lose, and you can even opt out of using Pokemon Showdown. Competitive battles happen when two trainers want to put their own trainer points and/or items on the line if they lose, and these must be done with Pokemon Showdown. League battles are sponsored by a certain type of Functional Organization called a Battle League; the leagues themselves determine what sort of prizes will be handed out, and you must also use Pokemon Showdown.[/indent]
[hider=Friendly Battles][u][b]     Friendly Battles:          [/b][/u]
The outcomes of friendly battles are generally discussed privately and concluded prior to the end of the battle, saving both parties involved the hassle of using Showdown. Theses are the only battles in which the usage of Showdown is not required. Of course, Showdown is an option, but should anyone wish to avoid the Showdown system altogether, you are welcome to just participating in a battle. The process of hosting a friendly, non-Showdown battle goes as follows:

[hider=The OOC Post][u]     The OOC Post:          [/u]
Each trainer will make an OOC post that includes participants (character and user), terms, and agreed-upon rewards of the battle. The terms include anything the participants agreed upon, including the number of Pokemon eligible for use from both sides and the posting speed you wish to set, if needed. Here is an example of an opening post:

[hr][h3]John Doe v.s. Jane Doe[/h3]
[b]Users:[/b] [@nobody01] & [@nobody02]
[b]Terms:[/b] Three Pokemon from either trainer, no items 
[b]Prize:[/b] 4 Pokeballs to the winner, prepaid by both trainers (2 Pokeballs each, 10CP per trainer) [hr][/hider]
[hider=The Battle][u]     The Battle Itself:          [/u]
The battle itself, because it is an informal battle, should be planned or discussed in OOC or over PM. The winner will depend on what either trainer wants, and if there is no agreement, Showdown is there as an option to resolve disagreements. 

Battle posts usually have two parts: the Reaction and Action phases. During the Reaction phase, trainers and their Pokemon “react” to what happened in the last post, dodging attacks or tanking them. In the Action phase, trainers and their Pokemon carry out an action — usually an attack— so that the other user can respond. Basically, battle posts are just normal IC posts. Use common sense and whatnot, and we’ll be fine.[/hider]
[hider=Ending a Friendly Battle][u]     Ending a Friendly Battle:          [/u]
A friendly battle is over when the trainers decide it to be, most likely in some prior PM discussion. After the battle has concluded, one or both users should tag me [@Dusksong] in a post so I can oversee the friendly transfer or rewards as well as check if rules have been followed. Whether the users want the battle to tie or be a KO to one trainer, that’s all fine. Should one of the participants of the battle mysteriously vanish, the other participant may inform me OOC or over PM, and we will discuss how to remedy this situation — most likely ending with the battle going to the user still active.[/hider]
[/hider][hr][hider=Official Showdown Battles][u][b]     Showdown Battles:          [/b][/u]
[indent]Pokemon Showdown: If you have never used Pokemon Showdown, be sure to familiarize yourself with the site before using it for this RP. For all Showdown battles, we will be using the "Anything Goes" format. When building your Pokemon, be sure to use the following guidelines: 

[list][*]One, use the same level, gender, and shiny status as listed here in this RP. 
[*]Two, refer to bulbapedia when choosing your move sets; only use moves that the Pokemon can learn through levelling up (unless you have bought and used a TM within this RP). 
[*]Three, only use hold items that you have purchased within this RP. 
[*]Four, there are no restrictions on setting a Pokemon's happiness levels, ability, or stats spread. [/list]
Once you have recreated your team on Showdown, simply click find a user and search for your opponent (let your opponent know if your Showdown name differs from your user name on this RP). From there, everything works just like the handheld games; battle back and forth until you have a winner. 

[hider=Dramatizing Battles][u][b]    Dramatizing Battles:          [/b][/u]
[indent]After your battle concludes and all awards are dealt out accordingly, you are encouraged to reenact your battle. This serves three purposes. One, it makes things more interesting for readers that haven't seen the outcome yet. Two, you still rack up one CP per post you spend reenacting the battle. Three, all Pokemon that participated in the Showdown battle and reenactment battle will earn two extra bonus levels. Finally, when the reenactment is over, provide a link so that people can re-watch the showdown battle if they would like. As we said before, you may skip using Showdown all together and only use post-by-post battling to Dramatize the battle, IF your battle is only a "friendly". If you choose to not use Pokemon Showdown, we encourage the participants to kindly talk through the outcome of their battle via PMs (this way the illusion isn't ruined for observers).[/indent][/hider]
[hider=League Battles][u][b]    League Battles:          [/b][/u]
[indent]League Battles can vary from League to League. They can use different formats on Showdown besides the "Anything Goes" format. They can have further limitations such as typing, tier, or level restrictions. Be sure to read the Battle League section of the "Create an Organization" thread. League battles will require the usage of Showdown, though, so it may be wise to familiarize yourself with the system before entering. Or not.
[/indent][/hider][/indent][/hider][/indent][/hider]

Hope that helped!