Is it possible and desirable to directly train the abs' strength?

Of course it's possible.

Now, the abdominals' primary function is to stabilize the spine. We see this because of its cross-hatched design. There is the rectus abdmonius, transverse abdominus, and obliques. These are oriented in different directions and so produce force in different vectors. Since the primary purpose of the abdominals is stabilizing the trunk, they can be strengthened by exercises where you must do this, like squats, deadlifts, presses, and Olympic lifts. Sine these exercises use a lot of weight, they are very effective at strengthening the abs.

Training the abdominals for athletics is more involved, since you also want to use them to produce directional force rather than use them only isometrically. So you'll want to do some special exercises in line with the needs of the sport.

Mike Robertson of IFAST in Indiana has written extensively on abdominal training. His material is a good resource.

Should I lift big to get big muscle?

Yes, you should, but not at the cost of your own inner core strength. You need proper diet, proper training and discipline to start lifiting heavy weight and in turn get big muscles. If you are someone who just joined a gym, I

How much protein should I get per day?

So I want someone to tell me based on what I ate today how many grams of protein I received. It would be great great as I am new to it and I am going to be really thankful. Also I want you to tell me if  that's

How to stay motivated to build a side business, when by the end of the workday I'm just too tired and frustrated from my day job

I think it really depends on the side business you plan to start. If you are already working a full time job and plan a side business, the side business needs to be something that you really love doing. You must have a passion for this business.