I agree with Daedalus about the prohibition around "move then action OR action then move" is to prevent movement being split and allowing abuse of the turn system by, for example, stepping round a corner, shooting a crossbow at a now visible monster, then stepping back round the corner, denying that monster, even if it is armed with a crossbow, the chance to get a shot back at you.
So, I agree the attack – move – attack isn’t prohibited in the rules or on the cards
Although perhaps it should be as allowing attack-move-attack introduces ambiguity in the card text in certain situations, for example Potion of Battle states” . . . It grants him 2 attacks per turn as long as there are monsters in sight. . .” so, if you permit attack – move – attack and you have a situation when the Hero is adjacent to a monster in a corridor and around the corner is a second monster, already placed on the board, then you could drink the potion when you have a monster in sight (adjacent to you) attack and kill the monster, at which point you no longer have any monsters in sight, so the effects should end, then you move around the corner so that you are adjacent to the monster, and therefore you now have a monster in sight, can you then take your second attack?
In terms of the same or different weapons, that is a harder one to answer in the context of the official rules as I’m not aware of any official rules around switching weapons.
I have my own house rules, below so as far as I am concerned the two attacks could be with different weapons, provided that my house rule is not broken. I don’t agree with Daedalus around applying the “you may only attack with one weapon at a time” rule in this situation, as there are two distinct attack actions (must be if you can separate them with movement), so each attack can only be with one weapon, but nothing prevents you from switching as you move between attacks
You may switch carried items (weapons and shield) as a free action only if you don’t have any monsters in the eight squares surrounding you.
Note: This happens automatically if you are armed with a ranged weapon and a monster moves into one of the eight squares surrounding you.
But this is getting complicated, and I don’t like complicated when it comes to HeroQuest as part of its charm is the simplicity.
Perhaps modifying the text for clarity and standardising the ‘two attacks’ text across the various cards would resolve this situation.
You could state that ‘…you may attack twice as a single action…’ which would eliminate the attack – move – attack situation, the multiple targets and the switching weapons situation amongst others or ‘…you may perform two attack actions this turn instead of the usual one action and movement…’ which would do the same but still allow you to use that attack action on a different monster that is next to you?