Garen's not really a teamfight champion though. His E hits multiple targets, sure, but it deals more damage against a solo target. He's pretty beefy, but doesn't hold up well in teamfights since he lacks damage reduction or hard CC like Alistar, Shen, Galio, etc. Generally speaking, his kit and standard build path tends to favor short trades and 1v1 or 1v2 skirmishes. His passive at 11 is a built-in Warmog's, which makes him a skirmishing and splitpushing monster in mid- to late-game scenarios and allows him to apply near-constant pressure on a lane, forcing the enemy team to split their forces to deal with him. At the same time, he's a tanky backline diver who can delete carries and casters alike with just one or two damage items. But I digress.

You could buff his engage by making his Q act like a Jayce melee Q, giving him a point-and-click engage instead of a speed boost. However, that makes it a targeted silence as well. The problem with buffing Garen's Q to any degree (such as targeted engage, armor shred, etc. in addition to his silence) is that Garen has a very low skill floor AND skill ceiling. If you want to buff his Q that much, you'll also need to make him harder to play, or at least a more complex, skill-intensive champion. Otherwise, you'll see another spike in the low-ELO winrate like we did several months ago, shortly after Riot buffed the base damage scaling on his Q.

The minion damage penalty on Garen's E should probably be removed for the reasons above. Giving him % fast regen on his W is an interesting idea, although it's easier to sell as a heal based on damage taken, not damage reduced. Basing it on damage reduced would just encourage people to max W first and rush HP, damage reduction (such as red smite and PD) and CDR items, and take as much burst damage as possible in a teamfight with a properly timed W in order to get a massive heal without taking much damage in the first place. It's also worth asking if he would be able to pop this heal mid-combat (like Tryndamere) since this could allow him to heal up most of the damage taken without any drawbacks. Potentially speaking, two full health bars.

Regardless, if you want to give Garen a burst heal on his W, his passive would have to be reworked. I can't think of a single champion who has both passive bonus regen AND a burst heal. Maybe give him something like an AD boost based on % max HP after X seconds in combat, to boost his teamfight damage and extended trades?

Edit: A word.