- Yes, just as it is written, your effective druid level to determine the Steed's power is as sum of your levels in Druid class plus your levels in Mammoth Rider class:
The mammoth rider’s class levels stack with other classes that grant an animal companion to determine her effective druid level.
Plus, from the Druid's description:
If a character receives an animal companion from more than one source, her effective druid levels stack for the purposes of determining the statistics and abilities of the companion.
- However, if you level up as a prestige class, you only get class features of that prestige class that are written on its chart, most of the time it means that you retain some of the features of your previous class, and sacrifice the others for powerful prestige class options. A common sacrifice is a bunch of caster levels. In your case (Mammoth Rider's description), for example, I don't see any information about spells and casting levels at all, which means that you get no new spells/caster levels at all if you progress through the Mammoth Rider chart. Essentially you sacrifice 10 caster levels of Druid for a bunch of cool features: by level 20 you will be Druid 10/Mammoth Rider 10, casting spells as level 10 Druid, facing level 20 enemies. I would call it a bad deal.
As an example of a class that keeps some spellcasting progression, look at the Dragon Disciple. This class is basically intended to be taken by Sorcerers starting from their 6th to 11th level. By level 20, as you see in the "Spells per day" column of the progression table, you lose 3 caster levels compared to 20 levels of the Sorcerer class: at 1st, 5th and 9th levels of Dragon Disciple you get no caster levels at all.
I suggest you to reread how the prestige classes work, what do you keep and what you don't keep, how are prestige class's BAB and saves applied, etc.