There will probably be more advanced rules for LOS from FFG some day. Till then, follow the rules or create some house rules for your gaming group and/or scenarios.
Q: In the rules, I couldn't find any mention of a maximum number of hexes that a unit can spot. This is only an issue for larger maps. I've been using the unit's long range as the max for this.
A: There is no max range. However, some scenarios might impose a limit. The reason for no max visibility rule is that TOI is a skirmish level game and so the distances are close.
Q: Is LOS determined by range or is LOS for a unit infinite as long as no obstacles are in the way?
A: Infinite as long as there are no obstacles in the way.
Q: Can a fatigued, pinned/disrupted, or Op Fire squad give LOS for strategy cards like "Sniper" or "Suppressive Barrage"?
A: No, for fatigued squads. Yes, for pinned/disrupted or Op Fire squads.