Others will come along later with more fluent answers than mine, but I can start you off.
140cm is the full width of the fabric, selvedge to selvedge so you should have some leeway if your fabric is 150cm.
It’s not usually good practice to use the actual selvedge edge.
You’re right about the grain, it is parallel to the selvedge.
The easiest way to think of nap is the texture on the surface of the cloth. Velvet, which has nap won’t match if the pile runs up in one piece and down in another.
Always follow the grain line on the pattern pieces and put them parallel to the selvedge. If a piece is cut on a fold, the fold should be parallel to the selvedge.
If you want to reuse a pattern in the future it’s best to trace off the size you need, keeping the original as a master pattern. It’s a bit of a faff but worth it for patterns you may want to use again.
You can buy dressmakers tracing paper but any paper you can see through can be used. In the past I’ve used cheap paper table cloths.
For your Burda pattern use View B and simply shorten the body pieces of the pattern to the length of View A before you pin them on your fabric.
The dog, I’m afraid is your problem, I’d just shut her out of the way but that might seem harsh to you.