The Tips menu option is the collection of tutorial pages and story details. It is not a hints and tips section. It is essentially the online rulebook so if you forget a tutorial about visions, for example, you can go back and check it.

STR: Affects the power of normal attacks
VIT: Affects defense
PSY: Affects the power of Gifts
DEX: Affects accuracy of attacks
AGI: Affects dodge rate
CRI: Affects the critical rate of attacks
MOV: Affects the distance one can move

This is from an old console rulebook. It seems vaguely right. A gift skill that punches an enemy still seems to use STR.

Each weapon has its own range. If the enemy is within range the enemy will light up. The weapon range is used for basic attacks, assist attacks, and I believe it is also used for defer between allies. Sometimes enemies within distance will not light up and are not targeted. This is generally because they are blocked by a wall, switch, or another enemy. In general, Gift skills have their own range regardless of the weapon.

There is no assist for area effect attacks. There is no retaliation for area effect attacks. This is true for both allies and enemies.

If you scroll to the right of the Gift screen you will see an additional skill for each of the character's three skill branches. These are unlocked for free once you buy all the skills of that branch.

There are a number of 'materia' skills in the gift skill trees. You cannot spend gift points to buy them or improve them, you just need to unlock them. You still need the materia or else the skill (see below) will be unavailable in combat.

To use a materia skill you need to get the materia in one of these two ways. Firstly, when you defer with a character you pass the materia from their skill chain. Secondly, fate materia items are found during the game that can be assigned to a character in their gift screen. For example:

If Shimano has bought a combustion skill, and not before, she will give combustion when she defers.
If you assign a sense materia item to Sho he can use an unlocked sense materia skill.