I'm sure this has been asked before, but I wasn't able to pin down an exact response beyond 'Maybe'.

A Combat Check uses the Fight stat. Does that mean that if an ability allows one to re-roll a Fight Check, does that also apply to Combat checks?

The same goes for Lore and Spells. If you are permitted to re-roll a Lore check, does that mean you're allowed to re-roll a spell check?

Like, the skill Wrestle. Once per turn, you can re-roll all 1s in a Fight Check result. Does that mean in Combat, I can do that re-roll?

You are correct.

All mods to FIGHT will affect COMBAT checks.

All mods to LORE will affect SPELL checks.

Awesome to know! So that means that 'Wrestle' and the it's Lore equivalent are indeed quite potent skills! 8D Much obliged, Gamemaster!

Boy, that phrase takes me back to that D&D cartoon! XD

just remember that the other implication is not true: Combat is a subset of Fight, so items, skills and so on affecting Fight, do affect Combat as well, but items, skills and so on affecting Combat do not affect Fight. For example, David Packard 's Comabt bonus does not affect rolls done for closing gates (pure Fight), but his Evade bonus will help you passing a check for Martial Law

Gotcha. So it's a one-way street then for sure. I started all this in regards to a newly created Investigator I am working on--basically, by giving said Investigator an ability pertaining to Fight, I am giving them a double-effect, since it works on Fight and Combat.

If I said the Investigator only gets a boost to combat, then they are, in a sense, only getting a single boost versus 'two'.

Aye, you got it

Same question came to me yesterday. One more thing: Does an ally or environment that gives you +1 speed, also give you +1 movement point? I assume yes, unless it specifically says +1 to skill checks. Which is the case for Minh's Synergy and Voice of Ra, so I'm pretty sure those do not give extra movement.

Be wary of the French translation. The translators made a mistake and used the word "combat" for both Combat and Fight.

Same question came to me yesterday. One more thing: Does an ally or environment that gives you +1 speed, also give you +1 movement point? I assume yes, unless it specifically says +1 to skill checks. Which is the case for Minh's Synergy and Voice of Ra, so I'm pretty sure those do not give extra movement.

Yes, you're correct, Environment cards boosting your Speed give you more movement points to spend; in the same way, Environment slowing you down, give you less movement points (this is usually stated on the card, though). Bonus to skill checks, instead, does not affect the total movement points you have (Synergy, Voice of Ra, and so on)