First of all I wanted to thank you for agreeing to take care of my dog and my house while I'm away.
Before I mention the tasks that I would like you to do here are my contact details in case you ENCOUNTER any issues. The name of the hotel is " The riviera" and my phone number is the 0212045126, feel free to ring me at any time. (you don't need up. To "ring me up" means to calculate the total of your purchases)
My dog should be fed once a day, the food cans are stored in the back of the closet just underneath the sink in the kitchen and the bowl is located near the front door, and please make sure the water bucket next to it is full as well.
While you're at it, could you also have a look at my mailbox and bring any mail into my house. (Mail is an uncountable noun. You can't add 's' to the end of it)
Thanks again and keep in mind that I will make it up to you as soon as it is needed.
In general this is good. There are some places where you used more words than a native English speaker would but I didn't correct them because they weren't wrong.
Also, I think the notebook section of italki is better for this kind of thing in the future.