[RPG] Do Druid animal companions go up in size with HD and gain size-based stat increases

I believe Savage Species, which is 3.0 but was the last thing put out before 3.5 and is therefore a pretty good guide to such things (and way more comprehensive than the blurbs in the 3.5e MM). It leads me to answer these questions thus...

1. Sometimes. Savage Species says about applying templates,

   If the template changes the base creature’s size, use the Size Increases table in the introduction of the Monster Manual to calculate changes to natural armor, Armor Class, and attack rolls. Check the text of the template to see if you apply size modifiers to Strength, Dexterity, and Constitution. The Abilities line may already account for those. Add all ability score modifiers, from size and the Abilities line, from the template to the base creature’s ability scores.

2. Not per se. When discussing how to come up with the LA of a monster, it says,

   Size: A Large creature gets no level adjustment for size. Its level adjustment is based on its reach instead. A Small creature gets a –1 level adjustment. It is somewhat harder to hit than a Medium-size one, but it moves more slowly and must use smaller weapons. A Small creature also typically has a lower Strength score than a Medium-size creature. Reach: Beyond 5 feet, every additional 5 feet of reach is worth an additional +1 level adjustment. A monster with a 10-foot reach gets a +1 level adjustment, and a monster with a 15-foot reach gets a +2 level adjustment.

3. If your GM allows it, anything's possible. You might want to look into Savage Species for more guidance. If he were to sign off on you being a Large gnoll with a starting ECL of 4 and a LA of +2, you could then have six character levels to cap out at ECL 10.

Yes, you increase Animal Companion's ability score when advancing it by HD.

The rules for Animal Companion bonus HD state explicitly which benefits it receives as normal for advancing a monster's Hit Dice. That allows to conclude, following the logic of the D&D system, that other benefits are not gained as normal, and therefore size and ability scores are not increased per bonus Animal Companion HD.

However, this article explicitly says that Animal Companions advance as normal per HD, except size. This raises a question of source precedence, and as for me, the mentioned WotC article specifically regarding Animal Companions is a primary source.

A quote from the article in question, for convenience:

Bonus Hit Dice.

The animal companion gains extra Hit Dice as noted in the table on page 36 of the Player's Handbook. The companion gains the full benefit from increased Hit Dice, including increased base attack, base saves, skill points, and feats. The animal companion, however, does not increase in size (any more than you do when adding Hit Dice for your class levels).

Note: Pathfinder Druid has this covered.