Is there a precedent concerning the showing of digital images to a jury?

This calls for opinion testimony which is given by experts who can be qualified by experience, use, industry proven accuracy. See IP litigation...

How can I claim fair use for unpublished video?

The Fair Use analysis requires advice from IP Counsel. Don't do it yourself.

What do I need to do in order to legally sell e-cigarettes/vaporizers online? ?

Contact the municipality, County and State where you live to get advise on permits et al.

Can I use a caricature of a famous person on a "gag" fishing lure without permission?

There may be a right of publicity or privacy. Check with IP Counsel.

Trademark Infringement question, Please advice

If the marks are used as Trademarks and your use is for similar goods or services then your use is probably infringing. See IP Counsel.

High likelihood of Copyright Infringement. See IP Counsel

The video, including the appearances by your dog, was not your work of authorship and hence not your copyright property. Does your dog have a...

Is this enough to go to court with ?

Perhaps its still not clear. the sentence "Critiquing the show or using some information from the show to make 4 min long educational videos."...

What Can I do In this Case?

You'll have to have direct contact with and analysis by IP Counsel re: litigation realities and damage assessment. See IP Counsel.

Is Giphy legal?

Unauthorized use of works os authorship may be copyright infringement. See IP Counsel.