1. Should I instead just up-pot into a 5 gallon (or 10 or 15) pot this year and give it another year before putting in the soil?
In my experience, the sooner an avocado can go in the ground, the happier it will be. Some do fine for a couple years in 10-15 gal pots, but I'd say go in the ground as soon as last chance of frost has passed.
2. When it eventually goes into the ground, should I make a "mound" within my raised bed, or can I just fill it up so the entire raised bed is the same soil level?
I'm not sure that I understand the question, but a raised bed is already a mound (relative to the surrounding soil level), you don't need to build up an additional mound of soil above the top of the raised bed.
3. What soil amendments should I use? My go to for my other raised beds is mel's mix (1 part peat poss (or coco coir), 1 part perlite (or vermiculite) and 1 part compost, and for other fruit trees I've planted, I've just mixed in a slight bit of compost into the native soil and they have all done well. I've read that builders sand is good, but I'm not sure if that's in place of perlite or in addition. Would love to hear some examples of soil mixtures others have used that have been successful for a raised/mounded avocado in the ground.
This is going to be highly dependent on the nature of your native soil. Since it's a raised bed, does it already contain amended soil, or is it just your local topsoil? Avocados can handle a wide range of soils but generally don't like highly alkaline soils, soils with high salt content, or any soil with poor drainage/high water table.
Here in the PNW, my native topsoil is comprised mostly of silty/sandy/clay-rich glacial deposits from the last ice age, and is very low in organic matter. I mostly don't amend the soil much other than to mix a bit of organic matter into the backfill (using a mixture of compost and composted manure), but I do top-dress with compost and then often add wood chip mulch on that when I've got some handy.
4. I assume that mulching w/wood chips or pine straw similar to other fruit trees is okay?
Not just ok, it's highly recommended. I don't know about pine straw, but some of the fungal pathogens that cause root rot in avocados are reduced by the beneficial microbes that flourish in wood chips.