Platinum uses the same evolution methods as Diamond and Pearl but expands the regional Pokedex from 151 to 210. More evolution chains are available before the postgame, including Fire-types like Houndoom that were locked to the National Dex in DP. The same 29 cross-gen evolutions are all accessible.
Platinum expanded the regional dex from 151 to 210 Pokemon. Fire types like Houndour that were locked behind the National Dex in Diamond and Pearl are now available during the main story. Same for Eevee, which you can get in Hearthome City before the third gym instead of post-E4.
Same spots as Diamond and Pearl. Eterna Forest has the mossy rock (Leafeon). Route 217 has the icy rock (Glaceon). Mt. Coronet's magnetic field handles Magnezone and Probopass. These locations don't change between versions. Just make sure you level up while inside the specific area.
Not quite all of them. Some cross-gen evolution items (like the Electirizer and Magmarizer) are tied to Pokemon availability. But Platinum gives you access to many more than DP did. The expanded dex means you'll have more evolution chains active during the main story rather than waiting for the National Dex.
You can get Eevee from Bebe in Hearthome City. Friendship during daytime for Espeon, nighttime for Umbreon. Stones for Flareon, Vaporeon, Jolteon. Level up near Eterna Forest's mossy rock for Leafeon, Route 217's icy rock for Glaceon. That's all seven Eeveelutions that existed in Gen 4.
No method changes. Everything works exactly the same way. The only difference is availability: more Pokemon appear earlier, and some item drops are shuffled. If an evolution required AncientPower in DP, it still does in Platinum.