As far as side reins at a walk, head over to the Dressage forum and look at the thread I started on side reins and following hands.
I had similar concerns about them restricting motion too much and ruining my guy's "Forward", and I got some excellent responses.
I would not
attach the side rein to stirrups. Far better off to attach them to the girth of your English saddle, or to a lunging surcingle. The stirrups will swing and negate the good side of the restricting action, not to mention they will just act like the worlds worst hands and jerk on the bit when they move.
If you're using side reins, use a bridle. Pretty much the whole point of the side reins is establishing correct contact with the bit, not a halter/cavesson. If you aren't using side reins, the lunging cavesson tends to be preferred. I've always just used a well fitting halter, and I've never had a problem with the horse not responding to it or running through it.
I have used an arena to free lunge, there's just a lot of space to cover. If the horse has never done it before, I would start in a round pen or get them very solid lunging on a line first. My first horse was very solid on a line, and when I free lunged him he was very capable of staying on a circle fairly close to me (i.e. Dennis Reis' Invisible Round pen) rather than barreling around the arena rail.
If you're starting the free lunging in an arena, I would say start with the line. Get him solid on a traditional circle and going through the normal roundpenning/NH lunging maneuvers there. When he's good there and really reading you, turn that circle into your arena's rectangle shape. It's going to be a workout for you, so a rope that's long enough for you to stay near the middle and do less running is a good thing. He'll need a couple of laps both ways to understand that nothing has changed, but when he's reading you again, go ahead and turn him loose. If it all goes to pot, go back to the line and prepare some more.
I wouldn't free lunge in tack. Some horses will roll when they get loose, especially in an area as open and dusty as an arena, and that puts some abuse on the saddle, not to mention the risk for getting tangled. If I free lunge, the most the horse wears is a halter. In a roundpen there's a little less space and incentive to roll, so maybe I'd roundpen with a saddle, but I'd still leave the halter. If you do roundpen in a bridle, take the reins off to avoid them getting tangled or stepped through.
Hope that was helpful to you, and good luck!