I have just started exercising and want to get rid of my belly fat. What should I do?

In this order:

1. Keep exercising, gradually increasing intensity and dosage.
2. Gradually clean up your diet with more veggies and lean proteins, less sugar and "bad" fats. 
3. Learn how many calories per day you need for maintenance and how many you're burning with exercise and start hitting these numbers. (you'll need to count and calculate for a bit, but the knowledge you gain is worth it.)
4. Define a proper ratio of macro nutrient intake and hit those numbers.
5.Give yourself several months to incorporate all this new knowledge and behavior.
6. Experiment with all of the above.
7. Never, never, never quit.

Why would my grip strength suddenly fail on a deadlift PR attempt?

Any number of factors could have affected your grip.  The bar or your hands may have been more slippery than normal, you may have used less chalk, your forearms may have been fatigued from something you did earlier in the day or on a previous day.  Without more context, it's really hard to say.

My advice is to try to attempt the 180, if you feel the rest of your "chain" is ready for the attempt.  It takes at least three data points to make a trend. So this one day anomaly should not be of real concern.  If you fail in similar fashion next week, it may be time to look more closely at the entire context of your dead lifts to diagnosis the specific problem.

I'm confident that if you approach your next session with a positive mindset, the weight is going to go up.

How do I get big and super cut?

Find a good low volume, full body workout based on compound movements. Do that three days per week. Stick with it for a year using progressively heavier weights.

Can I do two workouts in one day if I'm splitting between upper and lower body?

So long as each muscle group is getting adequate time for recovery and you're also allowing for overall central nervous system and systemic recovery, you will be fine.  Body part splits are really a matter of choice and you ought to experiment over time to see what different combinations do for you. 

Can I do two workouts in one day if I'm splitting between upper and lower body?

So long as each muscle group is getting adequate time for recovery and you're also allowing for overall central nervous system and systemic recovery, you will be fine.  Body part splits are really a matter of choice and you ought to experiment over time to see what different combinations do for you. 

You might even try working the same body part two or three days in a row and then allow a week or more to recover.  We used to call that "over reaching."  As long as you allow plenty of time to compensate and grow after the super-stimulus, you will improve, assuming overall rest and nutrition are adequate.

Can a Vitamin Deficiency Lead to a Bad Mood or Depression?

Recent research has linked Seasonal Affective Disorder (SAD: the winter-time blues) to vitamin D deficiency. Get some sunshine or supplement with vitamin D3, just to be sure.

On a more general note, lack of vitamins, minerals, phyto-nutrients, and polyphenols can all play a role in mood as can a calorie restricted diet. The mental depression that accompanies a slow down in metabolism is an evolutionary link that restricts activity in the presence of potential starvation.

Also, the blood sugar roller coaster of a high carb diet can play havoc with your mood.

Always keep your macros appropriately balanced to your activity level. Don't overly restrict calories. Always eat plenty of vegetables and fruits.

Should I do Cardio and Weight Training on the Same Day?

The bottom line is that it really depends upon your goals and where you are now in reaching your long-term objectives.

Very recent studies have shown that for the average person it really doesn't matter, after a "break in period of a couple of months.  Both strength and cardio health indicators improved to a statistically similar degree, whether you did one or the other first or whether you did them on different days.

Most successful "natural" bodybuilders will do their cardio either on an empty stomach, before breakfast, or after completing their weight lifting.  The theory being that once the muscles are depleted of glycogen, you're more likely to burn fat during your cardio session.

I personally do 15-30 minutes of cardio after each of my four weekly weight room workouts, in order to manage my body composition,  as well as several short walking and stair climbing sessions, during my weekdays at the office.

At the same time, because I am a multi-sport athlete, I also tend to do sport specific cardio, either steady state or HIIT on the other three days of the week. I don't find this to be onerous because for the most part, I'm doing activities that I love, either on the bike, one the road, on the slopes, or in the water.

Do what works for you.  Both cardio and strength training are important for overall health and sports success.  And unless you're working at an Olympic or pro sports level, it really doesn't matter.