Could I/should I do this on my own as a beginner?

My parents are interested in redoing their backyard - they want to take down the deck and put in some brick, leaving space for growing plants and flowers and possibly a veggie garden. I want to help them design and build their new garden, but I have zero experience with carpentry or construction. In theory, I could just read books and watch Youtube videos on deck destruction and brick-paving, and hustle my way through. I would plan to ask some permie friends for people that would be interested in helping out. But I'm not sure if that's really a great idea. What would you recommend? Should I hire an experienced consultant/construction company to do the deck destruction and brick paving? Or could I just go for it myself?

What I do have experience in is building veggie gardens and permaculture design, so I am confident I can fumble my way through that part of it and emerge successful.

Most of the time, just making the attempt is enough to get the job done.
You've not described the condition of the deck, so it's hard to say if you can do this yourself without more information. If it is not up in the air, made of common pressure treated lumber, does not attach to the home through the wall, it should come down pretty easily.
a typical deck is built by placing a foundation. This can be posts in the ground surrounded with cement. Beams are hung, connecting the posts. Joists are placed at intervals to support the deck. Rails are often an extension of the posts. Top boards and decking are screwed on top of the joists.

For deconstruction, work backwards.
Deckboards should come off pretty easy. Unscrew them, stack them neatly out of the way. You may encounter a rusted screw or nail here and there. Pry the board off. Any nails or screws in the boards can be removed so nobody jabs their hands or steps on them.
The joists may have galvanized straps at the ends. Remove these with a wrecking bar or pry bar. The joist are probably screwed or nailed in from the end. You may need to cut the joist for easier removal. Cut near an end so you have useful lumber for another project.
The beams will be heavier, get help, watch for nails and screws.
If the posts are in the concreted into the ground, you can cut it off at ground level. Get some help holding the post so it does not fall on someone or something.
To remove the concrete part, its all about digging. Those posts will be 2-5 feet down. With the concrete, they will be heavy. You can leave them and cover them, but this means someone in the future will have to deal with the mess. Same goes for digging a hole and pushing it over. Take it right out of there.
Where the deck connects to the house you should find a wide plank with big hex heads. These will be lag bolts. Back them out with a socket wrench. They will give you some resistance.
Take your time. Take a look at how it's built. Think of how things will fall, stay out of the way.

Decks are simple. It's just a bunch of boards put together in a specific way.
If you start to take it apart and find it's too much for you, that's the time to call for help.

One last thing.
If there is a door from the house to the shed, see to it the door gets locked, blocked, tagged, flagged, stickered or somehow secured so that people who might be familiar with the door don't step through it not knowing the deck has been removed.

For the brick walkways, a simple, traditional trick helps make them level:
Put an inch or two of sand down before you lay the bricks.
It is much, much easier to level a couple inches of sand than the earth itself.
(Plus, it helps provide better drainage if they are not mortared in place.)

If there's anything I've learned, it's that you can do it yourself. You may will screw some of it up, but what you will learn will be far more valuable than the price you would have paid to have someone else do it, IMO. The biggest thing I've learned is to try to see where your biggest failures will cost you and get some practice in on small areas before you get serious.

YouTube videos and other instructionals will get you about 90 percent of the way there, but how the mortar feels, how the brick sets, how to get the right consistencies in your mixtures are all things that will require some experimentation. I recommend mocking up a few small sections in low risk areas to get yourself used to the materials being used and to see how they will set up and sit in the coming weeks. Just about every time I go all in with a new mixture that requires curing I end up furious that I didn't practice with a smaller section to learn how the material works best.

Worst case scenario, you screw it up and learn a ton. Best case scenario, you end up with a beautiful backyard, you learn a ton, save a boatload of money, and get a little warm feeling inside every time you see it because you did it.

Also, like Ken said, if you are going to leave a two foot drop off out the back door, do something about blocking the exit or temping in a proper staircase.

All IMO, IME of course.