Depends on how sunny it is, how fast the underlying material drains and how frequently you need/wish to water. Both Irish and Scotch mosses like rich soil and plenty of water. Thyme likes it hot, lean and on the dry side. I am not very familiar with sun tolerant mosses although I'd suspect they'd be both hard to find and moisture lovers. Weeds will grow up through anything - you just need to be prepared to weed from time to time to keep things tidy. If using only the permeable sand then much easier to use some sort of herbicide to keep weeds in check.

I'm surprised no one else responded to this. While that would reduce the algae, or at least make it less visible, it would weaken the ability of the pavers to hold each other in place. You're 'supposed' to just sweep the extra sand away, leaving it almost even with the pavers. That sand will settle in eventually anyway, and need to be 'topped off' next year. I don't know what else you could do to prevent algae(probably moss) in a rainy climate. Learn to live with it, or bleach it?

I think it wouldn't be a difficult DIY project. It's a self-leveling compound, so all you need to do is blow the old sand out of the joint, make sure the mating surfaces are good and clean, then pour in the mastic. Deck-O-Seal is one of the products I've seen for sale on various pool sites, manufacturer's link is below. Here is a link that might be useful: http://www.deckoseal.com/system.htm

how consistent should the amount of sanding between pavers be? there are some on our newly repaved-with-pavers-lanai that look like they have almost no sand between pavers and other areas where the sand is flush to the pavers' edges... more gap areas than flush areas on the lanai edges are on either a poured footing or something that won't move like pool coping or house and are mortared down so "creeping" will be minimal but aesthetics and ability to trap moisture/dirt is increased with more gapping to my mind... the driveway done at the same time with same brand of pavers (but different color and style/pattern) has much more consistently fully sanded seams between pavers than the lanai... the lanai was laid over the original concrete patio which was not cracked/buckling so there is smooth base under the pavers... can't post photos here--don't upload to any site to link to but just want to know what the tolerance for gaps is with granite I know some people accept larger gaps in seams-- I had great granite guys that did my home remodel and seams were minimal--1/4 inch or less... had friend who had her kitchen done and she has noticeable seam that is maybe 3/8 of inch--and was told that was "good" job...