Is Hwei a reflexive trigger and when do you know when a card is a reflexive trigger?

No, Hwei, Brooding Painter does not have a reflexive trigger. His ability is a standard triggered ability ("When I move...") followed by conditional instructions that resolve as part of that same triggered ability.

How to identify reflexive triggers: Per Rule 387.1, reflexive triggers are recognized by the specific phrases "Do this:" or "Do one of the following:". Hwei's text says "do the following based on the discarded card's type" — that's a conditional branching instruction within the triggered ability's effect, not a reflexive trigger.

Reflexive triggers create new, separate Chain items when their condition is met (Rule 388.1). Hwei's branching effect (Spell → draw, Gear → ready runes, Unit → +3 Shield) all happen as part of the single triggered ability resolving on the Chain — no new chain items are created.

TL;DR for spotting them: If a card says "Do this:" or "Do one of the following:", it's a reflexive trigger and creates separate chain items. Otherwise, it's likely a regular triggered ability or inline instructions.