If you're worried about lots of cardboard in her poo because of chewing lots of loo rolls, try putting an empty (washed out) plastic milk carton on the floor for her to scoot around with and play with too. I've found that they last longer, are wonderful fun for a teething little pup, make a fab noise to keep them interested and don't cost very much!
With the biting problem. Sit down on the floor with her and let her climb all over you and play silly little games. As soon as she mouths you too hard, make a loud squeak noise (this will probably startle her) and then carry on the game you were just playing and give her a stroke (after she's let go of your hand, not before). This is how her dam would have disciplined her about biting and also how her siblings would have reacted during play when it got too rough. Basically the loud noise will startle her out of continuing to nibble you, and then the play starts again as soon as she's not biting you, so she learns that play is acceptable but nibbling isn't. She also won't get hand shy or frightened of you.
Playing with your pup is really important to build up a trusting bond between the two of you. Rigorous training at this age isn't really your main priority, the first thing you need to establish is a good loving relationship
With the toilet training. I would by-pass the puppy training pads. Instead just make sure that you take her out regularly to the garden for loo breaks and praise her when she goes outside (also choose a phrase like "hurry up" or "last wee" to say when she does go to the loo outside) This will help when she's older with asking her to toilet on command (useful for long journeys or if you've only got a short amount of time to let her outside for the loo). If there are any accidents in the house, just clean them up and make sure that you let her outside a little more often so that there's less chance of her making a mistake. Pups learn very quickly about asking to go outside for the loo if you choose to toilet train her like this
Finally the barrier is a great idea for across the sitting room area. If she does hop over it, go and pick her up and put her back in the area you want her to be in. If you catch her attempting to hop over the barrier I would say "no" or "off" firmly so that she stops and looks at you, and then chuck an empty milk carton in the area you want her to be in away from the barrier and say "go fetch" (or something similar) in a nice happy voice. This will make her feel your displeasure at her trying to get over the barrier, but will also immediately reward her for not hopping over and initiate a nice little play session in which you can build upon your bond with her.
Having time apart from your pup is also important. Even if it's just popping out to the shops or going into another room and closing the door for a minute or two. Your pup must learn that it's okay for you not to be there because you always come back again. Desensitizing your dog to you leaving them for a while is very important to stop issues of separation anxiety developing
Good luck with your gorgeous little pup
Best wishes,
Mary xxx