Just to clarify a few things.
Firstly, Vyse is not available to me yet. Maybe his arrival is random, maybe not. I'm up to chapter 9.
You can have a max of 20 members in your unit, but the actual number you can use in a battle is limited and depends on the battle / map. Around 9 or 10 seems to be the average. Before the battle starts, you select which units you want to use, and where you want them to start. Basic starting points are fixed in groups, usually about two, so you have two groups of troops starting from different locations.
Yes, there is a training area. Here you can use up the experience points you gain from battle (or don't if you perform badly). Here you can rank up your troops by category, so, you can say use all your experience points to rank up your snipers several levels, or you can spread the points more evenly across all groups, or whatever you like really.
You can also upgrade weapons and the tank in a separate R&D area. Doing this costs money, not experience points. You can upgrade weapons, clothing (defense), parts for the tank etc.
You can also use your points / cash to buy extra commands for Wilkin (sp) who is the main character and the tank commander. These are kind of like special moves that you can use on your troops in one off situations.
Also, you can buy news/gossip from the journalist chick. Doing this unlocks sub-chapters in the game. These aren't essential to the main story.
There are also museum/weapons encyclopedia/people encyclopedia sections where you can do a (ton of) reading up on the characters, weapons, and locations/themes etc in the game. You also get to play with the awesome 3D models in the weapon and people sections.
PSN - hanafuda