Visiting for 3 weeks !

Your SCUBA diving certification will depend on what course you want to take, as there are a few different types of certification. (PADI, SSI etc.) I think the majority are PADI in Vancouver. It will also depend where you're staying (proximity being important, I would guess). I would recommend looking for something that is at least 3 days if not 4-5, for a good base in the sport. It might be a bit cold for diving in the ocean, even in three weeks, even if you're properly outfitted in a dry suit. (They've been suffering a cold snap recently, that is uncharacteristic of the lower mainland.)

There is a decent library system in the lower mainland, using a linked system between different cities. You need to be a resident of Vancouver or one of the affiliated areas to get a free library card, though you might qualify for a non-resident card, by providing the appropriate ID and paying a fee. The downtown Vancouver Library (main branch) is a quite well known landmark that can be seen in many movies and TV shows.

I think socials for expats would be held in the various cultural centres (Italian, Croatian, Greek, Chinese, Japanese...the list goes on.) throughout the city. Being a native, I've never noticed expat oriented festivities. It is a very outdoor and active city, so there is always something going on - ice skating in Robson Square, the microbrewery beer tours, plays, music festivals, art shows plus tons of shopping, amazing restaurants and sports events.

Enjoy your visit.