I asked my dad for the gift for closing cost.

People who have been driven from their homes need things like dry goods, baby formula, water, diapers (for children and adults), toiletries, feminine products, blankets and jackets (cold weather is upon us), undergarments, shoes, gift cards for goods and groceries etc.The thing most people don't realize is that those who have lost their homes are looking at 2-3 years before they can rebuild, assuming they had adequate insurance to even rebuild at all.

They have a new puppy, I was thinking a small gift card to a Petsmart and also a check for $50 as a wedding gift. 

I think you should start by looking at your strengths and weaknesses.If you like to fix things then flipping and landlording are the way to go.If you like numbers and aren't handy, then note investing and mortgages are the way to go.What I'm getting at is that you can amplify your success if you combine your real estate investing with something you're gifted at. 

Is it cheaper to dissolve the company and re-create another one in her name or transfer (gift) ownership?

I got Diamond Reflection series cabinets with all-plywood construction at a lower price than either the mid-grade cabinets from the local kitchen designer or from the online order service from TimberPro (Floor and Decor) due to stacked discounts (20% off plus additional 10% back in the form of a Lowe's gift card that I will definitely use).

If she wants to give money as a gift that’s fine, just do it below the gift exclusion for tax purposes, but taking a loan is probably a bad idea

Should there be a separate company for the 'flipping or renovating business' i.e the flipping business is gifted the money by the trust, does the renovating and then sells the property back to the trust which turns around and refinances  (BRRR strategy) OR should they be one company? 

In the shopping center we have our own store occupying the entire space.My dad approached me saying he wants me to take over the store and all its assets for free as a gift,If I buy the building from him.

We tend to always send a 'Thank You' card along with a small gift card to Target or Starbucks.