TAG has many different options.
https://bg.battletech.com/forums/index.php/topic,82971.0.htmlRuns through all of the options for TAG. "Painting" and "successfully designating" are specific rules terms. As rules, TAG doesn't always have to paint (see the link). Lore wise, yes, TAG "paints" the target. Rules-wise, sometimes TAG requires the specific painting/successfully designating rules and sometimes it does not (see link above).
TAG can spot for any indirect attack (IF or artillery, p90, newly added to 6th printing), and can give a target number modifier for indirect artillery attacks (p47). It can also work with the semi-guided LRM (p150) and homing arrow IV (p152) optional rules.
NARC does not require indirect fire. It works with LRM, SRM or IF units (p87), whether direct or indirect.
Once a target is hit with NARC, any unit that attacks the NARCed target, and has the LRM, SRM or IF specials, does additional damage (p87). There is no target number modifier for attacks on NARCed targets.
NARC has no relation with semi-guided missiles. Semi-guided LRMs are a specific type of missile that works with TAG (see above), not with NARC. Lore wise, there are specific NARC guided munitions. Alpha Strike assumes if you have a unit with NARC, that your other units have munitions that can work with the NARC. So there's no NARC-guided munition rules in Alpha Strike.
Additionally, it acts like Artemis for missile launchers and gives a unit with NARC guided ammo a +2 to cluster rolls.
There are no cluster rolls in Alpha Strike.