Deck Previously Sealed with Thompson's Clear Water Seal

Greetings. 

I live and work in Greensboro, NC. I am bidding on a job to clean and stain a deck. Here's the pertinent info:

1) The deck is under fairly low light conditions. Lots of huge older oak trees shade it most of the day. It probably get most of it's light at high noon. 

2) The deck has been sealed at least a couple  times by the customer using Thompson's Clear Water Seal. The most recent seal, I think, was within the last 2 years. 

3) I did a water test on various location of the deck. I poured a bid of water on the horizontals at different places and for the most part the water absorbed into the wood. Some places it absorbed more slowly. Only up against the house did it not absorb completely.  The absorption overall was slow for all the test locations but the temps outside were about 70 deg F.  

4) I am still concerned that there is remaining sealant deeper in the pores of the wood. 

5) There are various varieties of algae/mold/mildew on the wood. From the picks, one light brownish variety dominates the surface and at first I thought that was peeling stain but it is definitely something growing. This is due I am sure to the deck not getting a lot of light and having a high moisture content longer after rains. 

6) The condition of the wood, however, is good. The deck is not that old. 

So, my first question is,  "Should I still use a stripper rather than a cleaner prior to staining?"

Secondly, "Is the Restore-A-Deck stipping product the correct stripper to use for this deck?"

Lastly, "Your recommended stain for this deck?

And note, I would prefer only an oil-based semi-transparent so I am suspecting that you are going to recommend the Armstrong or TWP. 

I am including pictures of the deck.