Yes you use your char and his skills/attributes, but use the gear of the army you're fighting for. You can also use any character now as your strategus character, but I believe there's a 7 day time delay before it switches to the character you want.
You can participate in strat battles without doing stuff on the strat map, but you need to have an avatar physically on the strat map before you can join a strat battle.
Typically (speaking from experience), strength heavy builds are better suited for fighting in strat battles (both due to sieges being the most important thing about strategus, and that most armies use very heavy armor). But I think strength heavy builds are the best infantry builds in general for crpg. I don't think it has much (if anything) to do with strat. If you said archers or something like that, then yes, I'd say that's heavily influenced by strat. But not so much any more that you can set an alt as your strat char.
I wouldn't say strat has diluted crpg at all. I personally enjoy strat battles more than public play on NA1 (even though I like playing there too). I think it's more fun due to having more organization in the fighting. If someone was no longer interested in playing crpg, but still played strat battles, that's not taking one from the other...it's simply just adding one to a column. But there are other people I know who only like playing in crpg and do not play in any strat battles. It's all personal preference, but I don't think one is detracting from the other.
