For number 1, I read or play a video game. I just can't get into solo board games. The closed I've come is with the D&D board games. I bought Temple of Elemental Evil. You can play that solo but it is very fiddly and much more fun with other players. Endangered Orphans of Clondyle Cove has a fun solo variant and is also one that your wife might enjoy as a two-player game.
For number 2, I have better suggestions as I'm in the same boat as you. I buy far too many games. My wife is not much of a gamer. She'll play games with the kids but the two of us rarely play a game with just the too of us. I find that card games generally are a better bet. That said, here are some good two-player games you can play with a "non-gamer" (i.e., someone that doesn't want the rules to come in the form of a small book). These are all games that I play with my wife and play with non-gamer family members:
1. Illimat. Kickstarted by the Decemberists and now sold from their Web site. My current favorite card game. Can be played with 2-4. Doesn't have a "geeky" feel and feels like a classic game but has some very interesting mechanics. Anyone who enjoys card games will like it and those who typically prefer board games will probably like it as well, be cause you play the cards on "board" of sorts.
2. Sushi Go. Easy to pick up but interesting choices and very replayable.
3. Ticket to Ride is a Euro Boardgame that many non-gamers like, but if it is too long or too complicated for your wife, check out the new small, cheap, and quick play version, Ticket to Ride: New York.
4. Kind of Tokyo. Great dice-battle game. Great for kids, but fun for adults as well. Maybe too cartoony and turn off some people.
6. Zombie Dice. Fun, fast, easy mechanics. *** Can also be played as a Solo game ***
7. Exploding Kittens, another fun card game that is great with two players
8. Bears vs. Babies. Fun, weird, but easy to learn and plays fast.
9. Endangered Orphans of Clondyle Cove, mentioned above, but worth mentioning again. Can be played solo, or with 2-4 players.
10. the Timeline Game (by Asmodee) series of cheap games that come in tin boxes are fun for people who like trivia games, but want a game that plays fast and is fun with as few as two players. They have many options. Everything from American pop culture, to general history, to inventions, animals, discoveries, etc. It isn't that replayable. After a few games you'll all know the order of things, but that also means you are memorizing history! And the games are cheap. Play a few times and give to someone else.
There are others but these come to mind without having to look up anything and these are all games that I've enjoyed with my "non-gamer" wife, parents, and sisters.