[RPG] Any Druid class variants that replace Animal Companion without degrading Wild Shape

Yes, the rules are scattered. Nevertheless, let's see what we can find out.

A Druid does not gain the bonuses to Strength, Dexterity, Constitution and Natural Armor listed on the Changes to Statistics by Size table. This is because the table is presented in the specific context of improving monsters by HD advancement. It does not apply in other contexts, such as a Druid taking the shape of another creature, or even an Animal Companion gaining bonus HD. It could be said that the Druid gains the "AC/Attack" bonus or penalty listed on the table, but that is because that column is just calculated from a table that is applicable - the Creature Size and Scale table.

The latter table is not restricted in scope as the Changes to Statistics by Size table. If I may dare say it, it is only logical that it isn't - these statistics are as basic as "Space".

Deriving from that table, we get answers to your specific questions:

1. No, that table isn't relevant.
2. Yes, the Druid's size modifier to hide changes.
3. Yes, the Druid's attack, AC, and grapple modifiers change.
4. Yes, the Druid's reach changes.

Note, however, that points 2-4 should already be factored into the statistics of the creature into which the Druid is Wild Shaping.

The half-giant monster entry lists Powerful Build as a Special Quality. Alternate Form explicitly lets you retain those, so yes, a druid with Powerful Build does retain that bonus, which is sizable. Powerful Build explicitly stacks with things that change your size, so if the druid used Wild Shape to turn into a Large creature, he would count as Huge for the purposes listed in Powerful Build.

See here for a list of options for obtaining Powerful Build. Note that all of them have positive Level Adjustment, which the homebrew lesser half-giant you found does not. Many DMs would balk at that. In reality, Powerful Build on its own probably doesn’t justify LA +1, but Wizards evaluated it as such. Level Adjustment is bad in general, but truly awful for spellcasters. And the half-giant race has nothing else of use or value to a druid, though use of the Primordial Giant template from Secrets of Xen’drik, at least, would make the half-giant more caster-ly (though still nothing particularly relevant to druids).