I didn't really read the replies, so if I'm redundant I'm sorry. :)
(This was all with the help and guidance of my trainer)
I'm training my mare now, she'll be 4 in April, I got her last January. I was going to teach her to drive first, but she was a little too nuts for it at the time. I'll tell you what I did with her. For the first month, all we did was lunge. The first couple weeks, just in a halter.. until she understood the voice commands. She would woah, walk, trot, canter all from voice, I didn't even need a whip.. and when I did I just lashed the end of the lunge line. (the whip sent her off) Then I introduced a bitting harness without the bridle.. first the surcingle, then the crupper. Then I introduced the bit, every day increasing in time she wore the headstall with the bit and no noseband in her stall. I let her loose so she could eat hay and relax but I kept my eye on her. I used a straightbar rubber loose ring snaffle, it was big and a lot to take in, but much gentler on her mouth then metal. Then I introduced the noseband. Then I lunged her in the full bitting harness with the bit for a couple days. I then added side reins very loosely, and slowly tightened them. Then we long lined for almost two whole months before we rode. I introduced other equipment, I would long line in a stripped driving harness, introducing each piece of "new" equipment as loose as possible, like the check.. etc. Long lining taught her to stop, turn, turn around, back, and three speeds at the trot. I tried cantering a few times long lining, but I would not suggest it with an inexperienced horse, just because it can get confusing at that point. Once my trainer and I felt she was ready, it was time to introduce the saddle. (After she became used to the bit, I switched over to a KK Ultra Bit long lining.. http://www.dressageforbeginners.com/...it/kkbits1.jpg
very nice and gentle for young horses)
I saddled her and walked her around the arena, she didn't seem opposed so I lunged her (just a saddle and halter). The next day I added the bridle, which she was plenty used to. She lunged like that a couple days. Then like you, I leaned weight in the stirrups several times. Then my trainer and I had a lesson where I got on the for the first time. She led me around at the walk and trot and we called it a day. The next day we did it again, starting on a lead and coming off when she was good. I would say keep the lead on as long as you feel safe with it. One of the next times I rode her, I mounted her alone and I got bucked off before other foot was in the stirrup. I was in a lot of pain and hobbled away because she started cantering around the arena.. when I felt up to it I went and grabbed her and mounted again, and rode her like usual. She has never bucked me off again, or sent such violent bucks.. but she has bucked and reared all of which I was prepared for. Lately she hasn't been bucking or rearing at all which is good.
Anyway, I would highly suggest long-lining.
You said he was green-broke? I took that as he had some basic training, I consider my filly green-broke but she does basic w/t/c work U/S now. Has he had any formal training at all?
As for the seven month old. It depends on their personality, but generally when horses nip me, I smack them in the nose and yell at them. Certain horses don't have the disposition for that though, and may become headshy. With my filly, I can't really do that since she's headshy already... but my gelding is the type of horse who would only become headshy if someone actually took a 2 x 4 and cracked him on the head with it, he doesn't care never has never will. It all depends on their personality. Chances are if she's ballsy enough to get nippy, they can take it back. It's playful, especially from foals.. If you don't want to smack her, then get really loud and scary.
I wouldn't carry a whip with you or use it, you don't want to introduce the whip as a punishing agent so young, because by the time you want to use it as an aid, she's going to have the preconceived idea that any time the whip is brought out she's done something bad.