a bunch of questions -- help!

As for the growling at other dogs I'll let someone more experienced answer that. I don't remember the background on your dog, so I wonder how old the dogis? She may be going through a fear period. It would depend on the situation as to what I would do. I would attempt to get her focus on me, with a "Look" command or a "watch me" command, which you'll have to teach if she doesn't already know it. Some suggest a down-stay or sit-stay while the other dogs pass. Were the other dogs on a leash as well?

2. my dog often rolls over onto her back when someone starts stroking her near the stomach or while she's lying down. my housekeeper likes to play with her when she's in this rolled-over position by touching her paws (which the dog sometimes waves towards whoever is petting her) and her body. lately though, instead of lying still like she usually does with me, my dog looks at my housekeeper and snorts and does an open-close thing with her mouth (not quite an air-bite) while following my housekeeper's hand. what does that mean? does my dog feel threatened when my housekeeper plays with her this way?

When my dogs go belly up for a tummy rub, they will wriggle around, legs often flailing around like they're trying to ride a bicycle. Often they'll make snorty noises, or play growl noises, and open and close their mouths. They typically won't grab my hands because they've been taught not to ( even though they may pretend to try to grab my hand). Sounds like fairly typical playing behavior to me.

3. when i am about to take my dog for a walk, it is difficult to put the harness on because she wriggles around, grunts and tries to avoid it, but once it's on, she's ok. how come? and before we are about to leave, she will snort, grunt and whine at everyone in the house. is it because she's excited? how do i get her to stop doing this?

Again, how old is your dog? Could be excitement. Trying to get four dogs at my house collared up to go somewhere can be a bit... chaotic. They have learned that they don't get a collar on (and thus aren't going anywhere) until they have a bum and all four on the floor. Sometimes takes a few minutes to get everyone settled, but it works. If your dog knows a sit command, I wouldn't try to put her harness on until she sits. Some of that may decrease with age. Personally I don't mind if my dogs get excited about going somewhere as long as the dog I want is sitting in front of me when I'm ready to put the collar on, and so long as nobody's mugging me in the process. A little roo-ing, prancing and snorting doesn't bother me too much.

The opening and closing the mouth is a submissive signal, saying "I'm harmless." Sofia does that a lot.

Is your housekeeper playing or teasing your dog? There's a difference. She rolls over to get a belly rub, which is a "I'm comfortable with you" message, also a submissiive one. You don't want to make that something that's NOT fun for her.

my housekeeper doesn't tease the dog, just plays with her. my dog is a mixed-breed who five years old and i recently adopted her from a foster.

I was wondering how things are progressing since you posted.  Also, how much obedience training are you doing with your pup?  Jules

hello,
 
i'm working on the obedience training. first getting her to master "come" and "sit", which i do on my own every day for a few minutes at a time. (there aren't any obedience classes where i live unfortunately.) she's getting more obedient though. putting on the harness is gradually becoming less of a problem as she is more patient and sits down to wait for me until i'm ready to go out of the house. no recent dog-aggressive experiences.