Welcome Aboard...Hope you have a great time here...
1. I've had mix feedback about building with Cedar if it's less than 50 years old. Supposedly it's not as rot resistant? therefor not as highly recommended. Does that mean I could get away with Doug Fir?
Well...??...there are regional differences with every species. Some say Cherry (Gen. Prunus) is "rot resistant" yet statistically, and through the historic record (for most regions) it typically is not resistant all...often less or the same as a White Pine ssp.
So, with your local "Cedar" (aka Juniperus, Calocedrus, Cupressus, Thuja, Chamaecyparis ssp...as the only true "Cedars" [Cedrus ssp] are found from the Mediterranean to Western Himalayan Region) so even a "new growth" variety will most likely be more rot resistant that a Douglas Fir. In general, of the species of wood you do have available to you...one of your "False Cedars" ssp will most likely yield the best results comparatively to others.
Now this is not to say you could not employ Douglas Fir or some other species. It all depends on how you are going to construct the Arbor, and what other methods are employed to mitigate potential rot. I am not sure if this is going to be some form of direct burial or other system The following are typically for least durable to most...which generically follows buried in soil (least durable)...concrete (which traps moisture and also promotes decay...chard, oiled and buried in gravel...or...above grade and fastened to stone?
2. The design I'm working with, is very simple, and with a Japanese influence. Any feedback on the shear strength (see photo's below). Should I add more braces?
Overall the design looks nice...
If going for an "Asian" aesthetic, such as a Torri system there are additional "horizontal" bracing beams called "Nuki" that could be added to the design to further strengthen the frame.
3. What sort of sealer is recommended for exterior exposed timbers? This will be traditional style joinery, so I'm concerned about the joints holding moisture in this oh so wet climate.
Traditional "garden" or "exposed" structures of this type are not "sealed"...on average all they receive is a really fine planing with a sharp tool and at best a natural oil blend...of some flax, tung, citrus, pine tar, oils, rosin and perhaps some beeswax. Joinery for exterior work can (and often was) design internally to shed water and/or some of the members would receive a copper or stone shrouding...
Hope that helped some.
P.S. Love the quote at the bottom...Simply outstanding!