This is all JMO and I know others will help too.
.... she will not do what she is told unless you have cheese.
How does she know? Is the cheese used as a bribe or lure? You might want to start real marker training, load your marker (a snap is OK, but I'm not that great at it, and would probably choose a verbal marker. I use "yes!", and I also use a clicker for teaching some things. But I would start with just one and get it loaded and very familiar. Do you have a bait bag?
So even if I try to get her to say stop jumping my husbands buddies I have to have cheese in hand or she completely ignores me.
What behavior have you trained her to do when you want that behavior to stop? Have you taught sit, or place?
The second thing she is doing is she will pee outside but we are in the middle of a room addition and with that addition is small bathroom which is not completed. She poops in there. ... why does she insist on pooping in there and peeing outside?
Probably, as pointed out, someone has punished her for a natural body function (pooping) when she had no option but to go inside. Now she has a perception that she must hide to poop.
Thank you and no I usually just snap. She responds well to that. I have never used a clicker before...not that I oppose it I've just never had one.
Do you know marker training? That is, did you load the snap? Do you always reward after snapping? You say "usually." What do you do other times?
We don't have a crate we do have a "bed" for her and she has been sent to bed and seemed to understand that she had done bad. She stole the chicken off of my stove top.
I looked at her and led her to the bed and said calmly "Bad girl. Go to bed and stay." She did!
I would not use her safe bed, her den, as a place of punishment.
I take her out about 6-7 times a day. Each time is for potty time and to run. We have five acres for her to run on and she loves it! I've been training her to stay within our property lines and she does pretty good but when another animal goes by she forgets everyhing!
She's not ready for that freedom, IMO. Do you have a long line?
So I've also been training her on the leash. For at least two hours she runs and plays chase, fetch and believe it or not hide and seek with my 8 year old. They have been caught rolling on the ground "wrestling" as well.
I would not allow this kind of rough play on the ground with a child after you have known the dog only a month.
I have seen her go number two but she will NOT go to the potty on the leash.
I would start a little log (a simple journal) of her poop schedule and make that the time for a good long walk (even if it's just in your yard), remembering that activity will stimulate peristalsis. I would be completely casual, however, since apparently she has been punished around pooping, and I would reward lavishly for each good event. Poop outside = party.
I've always been told that if you don't get on them as soon as it happens then don't know why they are being scolded? Is this incorrect?
I don't correct for inappropriate potty, period. It's a handler error. Sheila's post is right on. I'd tether the dog to myself and not allow any accidents to have a chance. That will also teach you her body language around pottying.
About the S/A, I would begin very casual 5-second leave-takings and returnings, then 10 seconds (and silent outside the door as if you had really gone) and so on. I would make both coming and going absolutely calm and no-big-deal. Then I'd do the same with both of you leaving, etc., etc.
After only a month, it's not a big surprise that she is anxious when she's left. I think that a combo of the proof that you always come back, along with increased familiarity and security are going to have big effects.
Congratulations on your new girl! I'll bet she's a terrific dog.