Can a player look at his own standing forces when not in battle? I assume yes, but the manual says the standing forces should lie face down and there is nothing about browsing them by the owner.

We allow it, with the provision that the forces are shuffled before combat.

Browsing is allowed. This can help in deciding what unit type to buy (sometimes). You can always get the opponents (or a neutral) to choose the cards at random prior to each battle if you're worried about someone cheating in the shuffling (you don't even need to be that good of a shuffler to cheat, since if you only have a handful of cards, it is easy to ensure your top card is selected).