Your agent will be able to answer all your questions and assist you with any of your arrangements.
But to answer your questions you've asked here, My Time dining is similar to going to a restaurant. You show up when you're ready to eat and they will seat you at a table with other passengers. While normally you'll have a different waiter and different tablemates every night, you can request a reservation if you find a table and time you like.
When you show up for dinner, if you have a particular table request like one near the window, small table, large table, etc, it could impact on the amount of time you wait to be seated.
As for tips for single cruisers, check your daily newsletter for all the events planned and definitely participate in as many as you want as there is something for everyone. Often, they will have a get-together for singles at some point during the cruise.
But the Oasis is an amazing ship with alot of activities and amenities unlike any other ship out there - I know you will thoroughly love the experience.