Not sure what the mooring buoy setup is in your case, however there should be a spliced eye in the connection to the buoy that you can run a line through and back to your bow roller, then onto your bow cleat / post.

12mm anchor line would be OK if doubled back to the cleat. My anchor line is very stiff nylon so to be absolutely solid on the cleat, I have often put some 6mm cord or similar over the top of the cleat to make sure the anchor line locking turns don't come loose.

If leaving the boat for a while, its a good idea to use something to prevent chafe on the spliced loop and your loop back to the cleat. Plastic hose etc should be fine.

anchor chain will be secure but wont provide much shock absorption. Make sure you lock the shackles with cable ties or similar to make sure the pins cant work out.

I'm sure others will be able to add to the above.

Congrats on your trip. Solo coastal sails are always an achievement.

I'm not sure which mooring you picked up but about 3 metres down the rope you picked up will be a swivel. You want to splice some 14mm mooring line to a steel eye and shackle it to the swivel I prefer the black mooring line from marindi but the white stuff from BCF will be OK.

Instructions on how to splice the rope can be looked up on youtube (thats how I learned to splice!)