Answer: Alright, here's the official word on attacks per melee (YES< THIS INCLUDES PALLDIUM FANTASY SECOND EDITION!):
If a character has no form of hand to hand combat, they start off with one attack and two non-combat actions per melee. If a character has a normal form of hand to hand combat (i.e. Basic, Expert, Martial Arts, Assassin, etc.) they get two attacks, plus those gained from the hand to hand combat skill (NOTE: Later editions and newer games dump this vagary for a simple 4 attacks per melee to start, as can be seen in the Rifts Game Master Guide and After the Bomb 2nd Editions). If a character has a Ninjas & Superspies/Mystic China form of martial arts (including the Agent hand to hand styles from N&S), they get only those attacks listed with the style. Boxing (and some special abilities) add attacks to any of the above cases.
Question: I never realised that a melee round got separated into attack and non-attack actions! I thought that an attack per melee meant an "action". For example, reloading your weapon is not an attack but still uses up attacks to do. So someone without a hand-to-hand skill really starts with 3 "actions per melee" out of which only 1 may be used to make an attack? In that case someone without a hand-to-hand could, for example, prowl up to a foe, surprise attack him once and (perhaps) subdue him and then prowl away. This would be the same as what someone with 3 attacks per melee could do only with 3 attacks per melee the person could have spent all 3 actions attacking, right? Also does everyone get 2 non-combat actions per melee on top of their attacks per melee or is it only a character without a hand-to-hand skill that gets this?
Answer: Melee rounds weren't separated until fairly recently, this kind of clear separation first appeared in the Rifts GM Guide (technically it first appeared in N&S, but since all the actions per melee were attacks, it was a moot point). Yes, someone without hand to hand training can only use one of those three actions to make an attack (though they get more attacks and actions later). Surprise Attacks occur only at the beginning of a melee round, though the penalties applied for attacking someone from behind would still be in effect in the scenario you describe. Only characters without hand to hand combat training get the two (initial) non-combat actions per melee.
Question: Also when it comes to calculating how far a non hand-to-hand character can move per attack, would we would divide his/her total movement per melee by 3 instead of 1 to give his/her movement per attack (action)?
Answer: Divide by three.
Question: Hmmm, according to p. 46 in the PFRPG rulebook, you can use your melee actions either to attack or to do something else... So I guess the above is simply not true.
Answer: Guess again. You can use melee attacks to do other actions, but you cannot use non-combat actions to perform attacks.
Question: Do you have the page numbers and books where all this information is provided?
Answer: Yes, as follows.
Revised TMNT, page 56: Attacks per Melee
Revised TMNT, page 57: Hand to Hand Combat
Revised TMNT, page 59: Melee or Melee Round
Revised N&S, page 165: "Do super-powered martial artists (like Physical Training) get two more attacks than their style's inintelumber?" [Basic answer without all the embelishments = NO!]
Revised N&S, page 165: "In Revised Heroes Unlimited, you automatically get 2 attacks per melee. Does this also apply to Ninjas & Superspies" [Revised N&SA was printed long before HU2E came out and hasn't seen (official) updating yet (HU2 has it's own reverse conversions, but there's not much to them). Basic answer is again, No.)
PF2E, page 46: Melee Action
PF2E, page 46: Melee Attack
PF2E, page 46: No Hand to Hand Combat Skill
PF2E, page 48: A reminder:
HU2E, page 68: Hand to Hand Combat
HU2E: page 69: Melee Action
HU2E: page 69: Melee Attack
HU2E: page 69: No Hand to Hand Combat Skill
HU2E, page 71: Remember...
RGMG, page 27: Attacks Per Melee
RGMG, page 44: Number of attacks per melee: (I'll quote this since it's especially relevant)
In the RPG and other books, it states that a character has "TWO attacks per melee to start." However, this does not include the two attacks per round any character with hand to hand training is supposed to start with. Yeah, we know that is confusing, that's why we post in these combat lists that the character starts with FOUR. So please do NOT add another two to this starting number. Sheesh, I hope this helps and does not cause more confusion. Example: A character with Hand to Hand: Basic starts off with four melee attacks, but has a total of 5 at level four, 6 at level nine, and 7 at level 15. If the Boxing skill is also taken, the character would have one more than those listed here.
RGMG, page 44: No Hand to Hand Combat Skill (note that this is NOT the first appearance of the 'non-combat melee actions' in Palladium).
ATB2E, page 143: Actions per Melee
ATB2E, page 143: Attacks per Melee
ATB2E, page 148: Number of attacks per melee: (While this is an almost exact quote from the RGMG (most of the HTH section is, with some actual fixes), there are suitable differences worth noting)
Most characters "trained" in combat start with FOUR attacks (the Assassin starts with three). This is consistent with Heroes Unlimited, Second Edition, Rifts and most of Palladium's other games. Over the years, there has been some confusion in these other games, but it is supposed to be four attacks to start. If you prefer starting with two, go for it.
ATB2E, page 148: No Hand to Hand Combat Skill
*TMNT=Teenage Mutant Ninja Turtles
*N&S=Ninjas & Superspies
*PF2E=Palladium Fantasy, Second Edition
*HU2E=Heroes Unlimited, Second Edition
*RGMG=Rifts Game Master Guide
*ATB2E=After the Bomb, Second Edition
Note: Newer games, such as Chaos Earth and anything else that actually manages to make it out soon will pretty much follow the rules set down in the RGMG concerning the attacks, unless the rules change yet again...