She will bring me a toy but then turn her head away with it in her mouth. I say give it to momma and she'll sneak a little look at me but then turn her head away again.
Head turning is a "calm down please" signal. She's come to say hi and has a toy in her mouth but doesn't want to give it to you. That's ok! Perhaps she'd prefer a bum scratch for instance.
Calming Signals by Turid Ruugas is a fascinating book that covers these sorts of things.
If I give the toy a gentle tug she will growl but her tail is wagging.
The biggest myths in dog body language are that growling is always unfriendly and wagging is always a happy dog. In reality it's hugely context dependant.
Growling can be a "fuck off" (and should always be respected, never punished, else you are likely to create a dog that goes straight to biting). Growling can also be part of play - such as a game of tug of war.
Wagging tails can be a happy dog (especially if a relaxed wag) but can also mean emotional arousal, and a dog that isn't very happy at all (eg reactive dogs will often wag tails very fast while scared and reacting)
Tug of war is a good game for building bonds - they can only play with you - but let your dog initiate - they usually present it to you - let them 'win' often and then bring the toy back for another round if they want to. It's possible your dog isn't ready for a game of tug yet and will only experience it as an attempt by you to take away something valuable, rather than as a game.
She will also growl and sometimes bark when looking out of the window , which is at other dogs going by, or neighbours putting something in their wheelie bin or whatever but again her tail wags.
Ditto what I said about the context of growling and wagging; this is guarding behaviour - normal but undesirable. I would keep the curtains shut or use frosted window film so that she can't see out and doesn't feel the need to guard her safe space.
She used to growl when we walked behind her when she was eating although that stopped a long time ago. She will occasionally growl and chase off one of our cats if he gets too close to her food, but other times she sits and watches him eat it! Cat is a greedy buggar and very dominant and 9/10 times puts dog firmly in her place.
Like most of us, your dog likes to eat in peace. I would ensure that she can eat away from humans and cats, for everyone's comfort and safety.
Likewise feed your cats in a high space the dog can't access.