How do the restrictions on battle form affect the dice that can be rolled together during an engage action, and how does changing battle form during an engage affect fatigue?

During an engage action, the battle form you declare determines which dice can be rolled together.
Battle form icons appear on skill lines, abilities, and weapon items. Only dice from skills, abilities, or items that match your current battle form can be rolled together in a single engage action.
If you are using a weapon, its battle form icon must match your current battle form to use its ability during the engage action (page 61).
Dice from skill lines with no battle form must follow the range of your current battle form unless otherwise specified by the ability’s text (page 61).

At the start of an engage action, you declare your battle form (page 59).
You may change to another form by marking the new form on your adventurer mat.
When triggering a class ability (not a standard engage), you may gain 1 light fatigue to change battle form before resolving the ability (page 61).
For standard engage actions, there is no explicit fatigue cost for changing battle form at the start of the action; you simply declare the form you will use (page 59).
However, if you are triggering a class ability as an action, you may gain 1 light fatigue to change battle form before resolving the ability (page 61).

Battle form restricts which dice (from skills, abilities, and weapons) can be rolled together during an engage action; only those matching the current battle form can be used together.
Changing battle form at the start of an engage action does not cost fatigue, but changing battle form before resolving a class ability (when using the class ability action) costs 1 light fatigue.

Sources:

Source: Core Rulebook (pp. 59, 61, 88)

Rulora