What to do about my adopted dog's behavior?

Whenever she looks to you nervously like that, talk to her softly. If she needs to stop a moment, kneel with her, perhaps let her sniff your hand. However, if she shrinks back at the sight of your hand, slowly pull it back to your side - don't force the comfort! Carry a few of her favorite treats with you on these walks to reward and encourage her, and eventually, the walks should become more enjoyable for her!

Remember, you don't know what kind of life she may have led before you adopted her, so always be gentle and encouraging. If you go a week or two and see little-to-no improvement, you should probably seek out a behavioral specialist. I wish you two the best of luck! She seems like a sweet girl. :)

You are right although she is still looking for you when offlead. Sorry to ask but were you not given advice that she shouldn't be offlead for about a month or so anyway so that you can be sure she will recall even when distracted.

However.... she is absolutely gorgeous and well done for taking her on. It is very early days and the best thing to do is just keep doing what you are doing and look for a little improvement every day. We get them into rescue much worse than this and it can take weeks / months to turn them around. I would say don't worry too much - yet, and just jolly her along when she looks sheepish. Could keep a few treats to give her.

I think she'll be just fine and looks like she'll make the perfect dog for you.