First time Dogsitting + dog with separation anxiety! Is this normal?

Hello! I'm so glad I found this forum because I would like to get some opinions on this experience.

I have loved dogs for a long time and usually get on telly well with most. I am more used to bigger dogs but have never had one myself before.

I decided to join a dogsitting site to help owners and at the same time get a feel for what it's like to have a dog. Now I'm on my first dogsit and it's a 3.5 years old Maltese. It's a good dog, he's obedient and follows basic things like sit, no , stay, wait ect. but he has quite bad separation anxiety. His owner told me about this, but as I am on holiday right now I thought it should be fine because I'll take him everywhere. I have previously read that separation anxiety dogs need to be in a crate when they are alone and the owner also said she had a crate that she could give me. When the day arrived the dog came with a pack of food, some toys, no sight of the crate. She said the crate was very big and that it was difficult to get it to my house. I was not very happy at all, as I think as a dog owner it is your responsibility to make sure the dogsitter has a safe environment where they can leave the anxious dog. Do you agree? Would you agree that she could have made sure to , for example, get a smaller crate she could give me? She just told me to put him in the bathroom when I leave.

I have the dog for a week. He's been coming everywhere with me and has been fine even with lots of people around. However, tonight we were at my boyfriend's house and some of his relatives were visiting, and the dog was acting weirdly, then suddnly threw up. I got insanely worried and messaged his owner, who replied saying that it was normal and that he has a verrrrry sensitive stomach and throws up about once a week. this is something she did NOT tell be before giving me the dog, I thought it was very irresponsiblee of her not to, as I have him for a week so chances are very high he would throw up. I was very stressed because he threw up on the carpet and of course my boyfriend was understanding but I was nevertheless embarrassed. I also feel kind of overwhelmed by the fact that I am responsible for another living being now, and I never seem to be able to completely and fully relax. It's Better when we are home and he's asleep but even then I stay anxious and I am NOT an anxious person at all normally! I have only ever experienced one period of anxiety in my life, right before I moved to university which meant moving to another country all by myself to a place I'd never been ect.. But is it normal to get so anxious about having a dog with you? I know I only had him for a week but I just with I could relax. Do you have any tips?
I feel like with the dog I can't live my life normally, because I don't have a crate to put him in and my housemates also use this bathroom mi can't leave him alone so take him everywhere I can but this also means I'm having to miss out on social activities like going to certain bars or restaurants and I cannot stand having my freedom taken away. It's like I need to fit my entire social life around the dog until it goes back to its owner!

I am 22 and still studying too, so I don't know if these thoughts are normal, or am I being selfish?

I am usually great with babies, but I am realising that with dogs my maternal instincts just aren't kicking in at all. The dog is also incredibly cute and is always staring at me and follows me around EVERYWHERE but I seem to be feeling annoyed rather than happy with him. this is also only day 3 of having him and I feel like there is forever to go until he goes home. I am regretting this decision to dogsit right now, I didn't think I would be that anxious. Please tell me if this sounds completely crazy pr if you've experienced similar things when being in sole charge of a dog for the first time!

Also, when arranging the dogsit the owner didn't specify a pick up time, and only told me 2 days before the dog was meant to come that she would only pick him up at 12 am or 1 am on the day after! I thought that was not very nice as I had made plans for the last evening. Please let me know your opinions on this too. Thank you sosomuch!