[Shop-talk] Determining beam span/hanging header joists?

[Obaa]

This is a follow-on to an earlier deck question...

I'm planning a 10' x 22' deck cover.  I plan on supporting it using 6 4x4 beams, spaced on both sides at the 1', 11' and 21' marks (10' spacing).
Would a 2x8 bolted to the side of the beams (or using those Simpson Strongtie connectors) be sufficient to hold up the cover without sagging, or should I plan for more support beams between the spans?
The cover itself will be made of 12 2x2 trusses (~9lbs each) and 11 roofing panels (~6 lb each), plus blocking between trusses.  I'm in an area with very little snowfall, but a lot of rain.  I'll need to climb up there as well to install the roof panels and flashing (~190lbs). Should I double up the 2x8's, one on either side of the beams?
The header joist will be made of 2 11' studs.  Is it sufficient to simply butt them together and center the joint overlap equally on the center beam, or is some sort of splice needed to keep them together.

Thanks for the help!