Own one doodle, getting another today! Need advice!

I'll try to keep this short.
We are probably crazy, but tonight we pick up a new doodle puppy. It happens to be free and was offered up to us and I couldn't resist. The basic story is that the breeder (hobby breeder, this pup is from her 4th litter) had this puppy leftover after it's sale fell through. She planned to keep him but then had a relative fall ill that she will need to help care for. She doesn't want/'have the time to go through her advertising and screening process for a new sale of him and so she put the word out to some friends. She is the friend of my friend who immediately thought of us since we already have a doodle. He is an Australian Labradoodle, cream with apricot highlights. Oh my is he cute!!

So...Marley (our current doodle) is an F1 that we re-homed from someone at 11 months old and she's now 23 months. She's got the typically nutty doodle traits, but has settled into a nice routine and can stay inside the house alone when we are all not home 2 days a week and doesn't get herself into too much trouble.

This will be our first experience with a puppy. I will need a lot of guidence from all of you experts. My overall concern is just how to integrate this tiny puppy with an adult dog especially when there will be some times each week that they are alone at home. Here are some of my questions-

1. Do we need to keep Marley and the new puppy (not yet named) mostly seperated? I would think they should meet, he's 9 weeks and his siblings left home last week and there are other dogs (his parents plus another) in his current home, so he's been around other dogs, but I don't know if Marley should really play with him too much. (He has had his first round of shots.) I'm just nervous that Marley will be beside herself with excitement to have another doggy in the house and play too rough with him and bother him or somehow get him sick. Or get nutty being seperated from him within the house. I assuming I should use the same consideration for a new puppy just like an infant child.

2. Marley's previous owner did not crate train. She learned to go to her bed and learned all the basic commands and was housebroken. In our house she has her bed, but has freedom at night to roam the house and generally sleeps on the floor next to our daughter's bed or on the foot of her bed. Like most doodles, she just needs to be near someone and give/receive love. The downside to this is she's often not ready to settle into bed until midnight or later and wants in and out of the house a few times before settling down. However we are getting a crate for the puppy and plan to crate train him. I'm just wondering if it's doable when Marley has a different routine? We wouldn't mind crate training Marley too, but she's so used to sleeping with our daughter I don't know how realistic it is to re-train her.

3. Our house is mostly carpet. I'm hoping to proactively minimize the accidents and will be diligent about potty breaks outside. With such a tiny puppy, do we keep him contained in a space using baby gates right now? I can't imagine him roaming the house at this stage, but there's a good section of our kitchen/breakfast nook we can close off with baby gates or even our master bathroom. And if we keep him in the bathroom, we can shut the bedroom door and keep Marley totally out of sight if that is what is best for both. Also, 2 days a week I'm at work so he would be inside all day. There's no one to let him out and neither of us work close by to come home at lunch. Is this a total problem? Marley has learned to control herself so I'm assuming we can eventually reach that with the puppy too.

Thanks in advance for the advice!!