My group's a bit confused about how movement works. Here's the list o' questions we have so far.

1. Do you have to spend a Free action each Initiative pass to run or just during the first pass? We think it's each pass, just checking.
2. To continue sprinting, do you need to to spend a Simple action each initiative pass?
3. Can you spend two Simple actions to crank up your Running Rate each round?
4. It says that each hit made during your sprint check ups your Running Rate. I assume that is your base Running Rate, before you divide it by your initialive passes to see how far you run in a pass, correct?
5. My roommate said that he found a rule mentioning that you can take an action anywhere during your movement. If so, could you pop out of cover (walking), fire a shot and duck behind cover again? I'm cool with that since it could be countered by delayed actions ("next time that guy pops out I'm shooting him!").

1-3) Not sure.
4) I would assume that to be correct, yes.
5) Seems to be the case. And since you can agree with him, why not?

We're trying to run the game RAW.

I'm fine with making judgement calls but I would expect movement to be a pretty set rule. And I'd hate to wing out houserules and find everythings already been clearly defined elsewhere.

Movement is seperated from the(free,simple,complex) actions .
If you were walking at the beginning of the round you'll be doing it throughout the whole round unless you switch Mode which is a simple Action IIRC from standing still -->Walking-->Running .
And while you're walking you can fulfill all of your actions.Sprinting is a simple action and adds +2 Meters per success to your running distance .
The total running distance will be divided by the Number of the one with the most Initiative Passes
Lets presume a Human with Base 25 Meters +1 success for 27 Meters who has 2 Ini Passes and an Enemy with 3 Inipasses. During each Inipass hell be sprinting 9 Meters even though he has only 2 IPs.In his first IP he'll be sprinting(simple Action) and maybe draw his Gun (second simple Action)
and moving 9 Meters.In his second IP he can Shoot twice and move his next 9 Meters and in the third IP ,even though he has no more Actions he'll be running the last 9 Meters
So
1) No ,its No Action at all
2) 1 Simple Action to sprint is all you need per Round
3) No by initiating a sprint Maneuver youll be sprinting the whole Round unless you Spend a simple Action to switch to "Walking Mode" or to a full stop
4) Right it adds to your basic running
5) Yes thats right :simple Action,simple Action ,free Action

HokaHey
Medicineman

In 4th edition Running takes a free action & sprinting takes a Simple action; sorry for not defining which system I was needing help with. I'll correct that now.

As for the example that I gave in question 5, allow me to paint the picture for you a bit better.
The scene:
There is an alley and my character is around the corner at the entrance to the alley. There are two goons that he is having a firefight with in the alley.
It seems that I can walk to the mouth of the entrance, fire two burst, and end my turn on the other side of the alleyway; all in one phase. This leaves the goons with no chance to hit me (because I'm going from a place of complete cover to another complete cover) with a bullet unless they delayed an action, right?

Huh, had an ASCII map made, couldn't get it to work right, sorry.

As far as i know, yes you can as long as it fits into the movement you can make in that pass. So if you are talking a human, elf or ork you have 10m walk movement a turn. If there are 3 IP's in the combat (not necessarily for the character) you could do this if the alley is less than 3.333metres across (10/3). For trolls it would be 5m, and dwarves would be 2.666m in that situation. I would require the use of a free action each time personally as it requires the players to change direction each time.
However, after the first time (if they are still standing) you can be sure as hell at least on of the opponents is going to have taken cover and delayed his action, just waiting for that runner to be in the open.

And I'm sorry that I didn't make it clear that I'm only playing SR4 too
once you Initiate Running(with the free Action) you can do other things while Running and you don't need to Initiate running again.Unless you Stop to "Walking Mode" or a full stop.Thats what I Meant with"separated from your other Actions)
Sprinting is a simple action because you give more Uuumph to speed up even more.
It seems that I can walk to the mouth of the entrance, fire two burst, and end my turn on the other side of the alleyway; all in one phase. This leaves the goons with no chance to hit me (because I'm going from a place of complete cover to another complete cover) with a bullet unless they delayed an action, right?
If they are surprised yes, of Course
even if not if its your turn you start walking,shoot and for the free Action Jump to the other corner of the Alley.You could even do it "John Woo Style": Jumping from one Corner to the other while simultaneously shooting with two Pistols.Its in the (SR4) Rules

with a Jumping Dance
Medicineman

However you do suffer those horrendous penalties for dual wielding....unless you use suppressive fire
Somehow i dont think it should work if you are trying to do suppressive fire with two machine pistols though. Especially with a single IP character . Would be awesome if a GM allowed it though

Awesome, thanks for the help gang, but I got another question.

Can a guy with 1 initiative pass change where he's moving to during a 4 initiative pass turn?

For instance:
My character is running down the road and fires a few burst on his action phase in Pass 1. He moves 6 meters.
The next phase the ground blows open 4 meters in front of him.

Does he fall into the hole?
Is he allowed to stop?
Can he instead switch direction and run 19 meters in the other direction?

Any option seems odd to me, especially for a guy that can't jump, go prone, etc.

I´d make it so that the character gets a free chance to react as an interrupt, drawing the next IP if an action is required, or changing the movement path for free.

unless (s)he's a blonde than (s)he has no chance to react ,even if its two Rounds til (s)he'll drop
otherwise I'm dancin' with Ryu
If you can drop Prone for a free Action ,I think it's Ok to change direction for a Free Action too

HeyaHeyahEya
Medicineman

Free Actions still require an initiative pass.

To make things easier(!?) in my game, EVERYONE can move on all 5 passes (curse Unwired!). It chunks movement up nicely so that you don't have ridiculous inconsistencies between the 4-Pass dude and the 1-Pass dude.
I had never thought of the "Switch Mode" Action being used for movement before. It would be nice for a Sammie to be able to Sprint to cover on Pass 1, switch mode to Stationary and Fire a Burst Fire on Pass-2 without suffering Running mods. It always seemed artificial to me that you would count as Running for an entire Turn, even if you stopped moving after the first Pass. I like it!