1) Groundwork. I think it is particularly critical right now, and it sounds like you do too. Any time a horse has a major change (like a new owner, or even a new boarding stable), let the horse guide you as to when they are comfy being ridden. There is no shame in waiting days or even weeks until you really feel like that horse is ready to be ridden. Rushing things has no place with horses. In the meantime, do your groundwork.
I do not do a ton of groundwork with my horse, but when I do happen to do it (with her or someone else's horse) I really like Clinton Anderson's groundwork excercises. Now he is not my guru or anything, I just really see a lot positive about his "lunging for respect" as well as some of his desensitization and sending excercises. Everytime you get your horse to move his feet, you establish yourself as more and more of a leader. I cannot describe all his methods, I watch him of RFD TV, but if I were you I would invest in some of the DVDs.
2) Grazing and treats. I am going to address how I handle both. I give treats specifically as a reward for certian behaviors, not just "because". Some horses can handle treats, others get nippy. Often though, limit setting can prevent the nippies from ever happening, so read how I do it and see if it helps.
Regarding grazing....this is a respect thing. Your horse is doing what she wants and ignoring your wishes. Little hint here.....gaining a horse's respect is usually an ongoing process. They will typically give you little tests, day to day just to see where you stand that day, same as they do to each other. Your job is to set clear and consistent (and fair, IMO) boundaries.
All horses like to graze, especially if they have no grazing in their turnouts. I am going to describe how my horse behaved with me yesterday regarding grazing and treats, and how I responded and why. This was when I went to get her for grooming and saddling. She also loves to eat grass BTW, and has been off due to injury for several months and has been testing me more than usual, so maybe it will be helpful.
I go into her turnout. She immediately walks over to me. I give her a treat (for coming to me). BTW, my treats are those tiny hard nuggets. I keep a handful in my pocket. So, halter on, I lead her through the gate and go to shut it. Her head starts to go down for tasty grass. I immediately stop messing with the gate and correct her with a quick jerk on the lead and say, "Head up mare! Be polite, remember?". She remembers. She licks and chews, telling me she got ghe message and stands quietly while I do the gate. Now we start waking a little ways and I say, "Ok, girl, I know you are dying for a bite, *now* you can graze." We stop for a minute and she indulges. Then I firmly pull her head up, say, "Enough. Let's go". I walk quickly and assertively, either at her side or even slightly in front of her. I do not look at her. She must know I am the leader, I know where we are going, I will be taking us there. On the way, I feel her head start to drift towards the grass. Immediately I jerk on the lead, before her head even gets near the ground and we walk on. She licks and chews again as we walk along, thinking about that correction.
I tie her to the rail and begin grooming. She is quiet and well behaved. I speak lovingly to her and spend lots of time currying and loving her. She is in heaven with her eyes half closed. A friend comes up to chat with me. I pause for a minute and turn to talk to her. My horse gets impatient and nudges me to tell me to get moving. Reflexively I smack her muzzle, pretty hard, and speak sharply to her. I do not like being nudged like that, and my horse knows better. *I* get to decide if I am going to talk to friends and take a break from her...not my horse. After being slapped, she drops her head and licks and chews (hmmm...mom was pretty serious about that). After her correction I move on and finish my grooming, just as lovingly as before. She continues to enjoy it to as though nothing happened, but we both know I just asserted myself, and set a limit with her.
I begin tacking her up. I do everything gently, but confidently. I never creep around my horse as though she might spook. I need to act as though what I am doing is normal, safe and I know what I am doing, otherwise she may think that either the situation is unsafe, or she needs to take control if she thinks I don't have control. When the time comes to bridle, I take my time. My girl loves having her head rubbed with her halter off, now is a good time. I rub her head and massage behind her ears. I slip the bridle on gently, she opens her mouth for the bit.
You mentioned taking the bit was an issue. If she did not open her mouth, I would have gently slipped my thumb into the bit space in her mouth to open it, and slide it in when her mouth was open. If she really resisted, I would practice bridling with a treat after she took the bit, or put a bit of molasses on the bit to make it tasty. First things first though, any horse that resists bridling should have their teeth checked. Also, ask yourself what kind of bit you are putting in, and how are you using it? I see horses get resistant to bridling after I see their owners riding them in strong bits that they are using roughly. If you use a strong bit, you need to know how to use it without hurting your horse.
This brings us to neck reining. If you are using a snaffle, direct reining should be fine right now. Do lots of side to side flexing (Clinton teaches this too) to get your horse soft and responsive. Lesrn how to release your flexing when she softens her head. It is also a great respect builder. Neck reining is more appropriate with shanked bits. It is hard to direct rein a shanked bit because of the leverage created by the shank. If you are a beginner and your horse does not know how to neck rein, I would stick to a snaffle and direct rein her. You can teach her later if you wish. I also think a snaffle is safer in some respects. If you get into trouble, you will need to get control of her head laterally and it is easiest to do that in a snaffle, again, because you have no leverage issues interfering with your communication to her.
Lessons. Nothing wrong with taking english lessons. Good riding is good riding. Also, an english trainer should be excellent at teaching you direct reining as opposed to the neck reining. Your lessons should help with your bucking at the lope issue. In short, the way a horse takes off in a canter departure, physically it is easy for them to throw a buck in there. It can be a physical pain thing, but is usually due to high spirits or reluctance (yeah, I'll canter, but watch me throw this buck in). Personally, I solve it by speaking sharply to them and driving the horse forward with my outside leg. Hard for them to buck if you keep them moving. Also I would do multiple departures to continue working on it.
Whew...I hope that helps. The reason I gave you the scenario with me and my horse is that I wanted to show that 1) All horses will test you in some sort of ongoing manner. The more you work with them the less they will do it (my mare is testing more because of having had lots of time off, but I have owned her for 8 years). 2) You can set limits, and your horse will still love you and enjoy your company. I did smack my girl yesterday. I rarely do that, but she rarely nudges me like that. It did not harm her. She kicks and gets kicked by her pasturemates a heck of a lot harder than my slap. 3) You can usually feed treats for specific behaviors, but watch for warning behaviors that could lead to biting (like nudging) and nip them before they get dangerous. 4) The key to correcting behavior in a horse is to do it quick and serious. Try not to let your horse get a few mouthfuls of grass before you correct her, get her before she gets anywhere close to putting her head down. 5) It is possible to set limits without being a dictator. Grazing is a real pleasure for my horse, and she does not have it in her turnout. I make time for her to graze, but it is on my terms, not hers. That is being fair, and I think we should always try to be firm, but fair.
This is just how I do things, I am sure others have other ideas. Sorry so long, but admittedly, your question was very long