You've got a lot of different questions here. Hopefully I can help with some.
The first thing that jumps out at me is that your dad's company is a sole prop. I could be wrong, but I'm not entirely sure you can have a sole prop as an umbrella company. And if you could, I would guess that you would also have to register your company as a sole prop. That means you would have no liability protection! You can offset that risk by purchasing liablity insurance. (This is something LLCs and Corps should also do anyways).
As far as your tax questions, it'll be hard for most of us on this site to give you reliable advice because you're located in Canada. I can tell you that there is no avoiding taxes...you will have to pay taxes. There are different types of taxes (and fees) and as a sole prop, you may be able to avoid some of the taxes an LLC or Corp would have to pay, but you'll still have to pay some taxes. For example, in my home state, LLCs and Corps pay a yearly $300 fee just for the priviledge of doing business in the state. Sole Props do not. But when it comes to income taxes, all entities (both businesses and people) are required to pay.
How does the taxing works? I am not selling anything, just making revenue from advertising.
If at the end of the year you net a profit, you will have to pay income taxes. How you made money doesn't matter...what counts is that you made money.
Also, will I have to pay taxes? What are some benefits of registering other than preserving brands (I am aware of obvious things like, you gain trust, things like more opportunities such as B2B). Should I even register if I just have to pay taxes? What are somethings that will happen once I register? I have to report everything?
This scares me. I could be misunderstanding your question, and if I am, please do clarify. But the way I'm reading this leads me to believe that you think you won't have to pay income taxes if you don't register your company. That just isn't the case. Everyone is required to pay incomes taxes on the amount of income they made in the year. This includes both individuals and companies. Now it's possible that in Canada there may be extra income taxes levied on businesses, so you may have to pay more taxes as a business entity than an individual, but you'll still have to pay income taxes in either case.
Again, I can't give you concrete answers, but hopefully I was able to clarify a few points for you. I added the Canada tag to your question. Hopefully that'll help you get more specifics to some of your questions.