The leaks might be because the plywood deck is spanning wider than a 2' span which the plywood might not be rated for. Crummy framing can make it impossible to not have leaks. Just like a bad flashing job often causes leaks. Watch that Holmes fellow from Canada doing remodel repair shows on cable if you want to see a hundred ways to do a job the wrong way. No not the way Holmes does things but all the screwups he turns up.
If you are serious about building you do not go to Home Depot or Lowes for framing materials. You go to a lumber yard. The lumber yard that supplied my barn and the one that supplied my house are gone but there are still 2 good lumber yards within 15 miles of my house. Or if you know what you want you have Lowes or HD order what you need. When I built my pole barn I bought 6x6 PT 16' and 20' long. I dug holes and picked them up and tipped them in the holes by hand. It sounds like you can do that but the inspector wants to see what you put in the holes. My inspector didn't seem to care but that was 13 years ago.
I am going to have to disagree with about everything you just said.
First, I believe to OP never made mention about using plywood. He is probabally going to use steel like 99% of pole barns today use.
Second, he never said anything about spanning more than 2' either. He said the purlins were GOING to be 2' appart, so I dont know how you got more than that.
And finally, the comment about "if you are serious, you dont go to a box store" kinda pieves me. What is the difference between a SYP 2x8 at lowes vs at a lumber yard??? The only difference that I have found is that the lumber yard thinks they are worth twice as much.
Their is absolutly nothing wrong with buying building material from HD, lowes, menards, etc. And no thanks on the special order or deliver either. I will pick the lumber I want off the rack. That way I know what I am getting.
To the OP: I see nothing wrong with framing the way they show in the pictures. Just be sure you size the lumber accordingly. Their are plenty of usefull charts and calculators online. The "purlins" that are going to be ran parallel with the ridge line will be easy to figure based on span. But the MAIN rafters these tie to may be a little more channenging. You have to factor the loads that are going to apply over the given span and treat it as a "BEAM" and NOT a rafter. Because most sizing tables for rafters only go up to a 2' span. And you are talking on the order of 10-15 feet. Personally, for peice of mind and it shouldnt cost much, consult a PE in your area. Take a pic like the one you posted. Give him sizes and spans and ask him how big the lumber needs to be. Maybe a 2x12, or a double 2x12, who knows. But get a PE's advise in that area and you will sleep better at night. That is of course if you choose not to use trusses or traditional rafters.