I would love to have a way to at least see other people in your faction. Lol I know a bunch of people that are Sentinels but I know very few Advocates.

Also on the Log -> Battle section, can you reword it to Challenged by _________ for when they attack you. I also don't think your attacks are Logged either which would be nice.

Standardize the Hi-Five times so that there is a daily reset for them all, I personally hate the 24 hour individual clock cooldowns.  

Developing on TheFiendish's idea..

Allow us to sell.
literlity everything. runes/fragments to materials to even magimons if people are willing.
Let us make the judgement on if the item is uselss or not...
I do have lot of useless runes that i dont even want to use for enhancing because i have better runes to enhance with.  

I'll go down the list:

Character leveling: Currently exp can only be gained through questing, making the notion of using battle to farm somewhat outdated as quests offer silver, items and experience. Battle system should give experience.

Communication: there has to be at the very least a personal message board set in place as playing an online game with yourself is somewhat monotonous.

Sell feature: some monsters I receive, I just have no need for. I'd rather have the option to sell those I don't need in order to build a silver cache.

Battle system: the battle system should be expanded to give the option of actually watching a fight, as the battle info is drawn out and hard to comprehend. Daily battles should also be limited vs the same player.

Magimon leveling: 500 Silver is far too high a cost to fuse two lvl 1. This should be scaled to reflect the monsters level. Experience gained through fusing a lvl 1 to a higher magimon is also flawed, and should function similar to MP.

Fragment battles: the pop up that advises a player to set a trap gets annoying quickly, and should be minimized to an optional click.

This is what I've got for now, I plan on continuing to play so I can help improve your system.  

The localization of the cat Magimon when viewing the sample Magimon should be adjusted. As it stands, the cat Magimon suggests that the ones shown are the only ones that can be created based on what he says "This is the Magimon you can craft with this cauldron".

Perhaps change to - "These are some Magimon you can craft with this cauldron"

I know it's implied since we are clicking "View Sample" although I was mislead when I started playing and the cat Magimon's text would affect my decision to use that cauldron because none of the Magimon shown interested me. As I created Magimon and realized I was getting Magimon that weren't shown in the "View Sample", I realized there were more Magimon I could get.  

I like lots of suggestions here! Here are a few more:

1. Provide an alternative way to spend energy that doesn't earn Player Xp!
a. Train Magimon - spend Energy (and Silver?) to earn Magimon XP.
b. Scavenge - Use energy to search the Areas for silver/objects/gold (no player xp)
c. Buffs - Use energy to buff your next battle (NPC/PVP) ie. 10en for 10% HP buff, 20en for 10% PWR buff etc...

2. Give us an option to choose how we want to see battles.
a. Quick (as is now)
b. Full (same as now but will all steps played out)
c. Skip (skip the animation and just go to win/lose)

3. Put a big warning on Evolution Screen that says that the levels for combined magimon will be reset to 1. I flipped when i lost 8000+ silver when I evolved my level 16 magimon Still very upset about it since there's nothing that i can do about it.

4. Allow a 1 time point redistribution available after level 20 (available for a few days?). When you're new you have no idea how to spend your points and since you can get through half the levels in only a few days there's nothing you can do about it afterwards.