Strength is the key to long lasting tile installations and plywood and Durock are the strongest underlayments you can use. When bonding tile to plywood please use a quality setting material like Kerabond/Keralastic.
The screw pattern is important with 3" drywall screws every 6 to 8 inches down the floor joist and 1 5/8 drywall screws between joists. Tying your installation to the house with 3" screws is the strongest thing you can do. Start at one end with the screws and work your way across the sheet so underlayment takes the contours of the sub-floor. All older homes sag to some extent in the middle of the room. (For example you don't want to fasten all the floor joists first.)
It doesn't matter if sheets are butt together, with the amount of screws the plywood is not going anywhere. For sure you want to bridge all sub floor seams with the plywood underlayment. In this case the existing floor is old vinyl asbestos tile that was stuck very well. If it were loose I would have taken the V A up.
For Durock, 100% bond with mortar. Add a 3" Drywall screw every 12" and big headed roofing nails inbetween to make sure Durock takes the dips and valleys of the sub floor.
After the underlayment is installed, place a straight edge across room to see how much leveling you have to do. In this case, about a strong 1/8 in the center of the room. I've had old farm houses that a whole strip of 1/2 Durock would be under the straight edge. It's a fact all rooms sag in the middle as they age and if you want your installation to stand at attention, you have to level.