Need advice on Nikon D5200 video shooting

Update: Please check the first response and give me some critical feedback!! I want to know if I am potentially fixes this issue or not. Thank you!

I have a Nikon D5200 with the 18-105mm lens.
How do I take HD quality videos? Whenever I take videos of active sports/events, pulls of my car, or everyday activities, I can't seem to keep the video in focus. It is only focused at the beginning then the rest of the video will somehow blurred out overtime.. I am a beginner at DSLR cameras, so any advice helps. Thanks..

I also wanted your guys opinion on a few more things.

What is a good all around, easy to travel with tripod?

I plan on purchasing the AF-S DX Nikkor 35mm f/1.8G lens. How does this lens pair with the AF-S DX Nikkor 18-105mm f/3.5-5.6G ED VR lens?
I am attempting to look for a good all around pair of lens. As an amateur, I believe this combo would work wonders as the 35mm lens will provide optimal scenery shots(especially in the city),and the 18-105mm lens will provide just about every aspect of shootings with its decent amount of variable zooming.

Hopefully these questions make sense, and thanks in advance for the help

I think I might have figured out my problem, I have only created a few videos before I read the manual and looking up advice online. I was shooting the videos in auto format with lower aperture, I might have attempted to refocus during each video to accommodate poor quality, and I have always attempted to auto-focus. I believe that if I instead did the following, it will make the quality more bearable and less blurry.
Create videos in the A mode (or P mode), manual focus before I start the video (or auto-focus in some cases), try to remain as steady as possible when taking the video, and use the 18mm on my lens instead of zooming in.

Whenever someone can, please correct me if some if not all of these potential fixes are wrong. Also, still need advice on the last two questions of this post