Fixed means a range expressed in a set number of feet, eg 0ft or 60ft, as opposed to a range like Close, which varies depending on level.

There's a big debate as to whether touch spells count as fixed, with some evidence on both sides. Personally I'd advise against it as it makes an already awesome feat ludicrously powerful.

Yes, Divine Power is one of the classic DMM: Persist spells. Others include Divine Favor, Holy Star (SpC), Greater Visage of the Deity (SpC), Elation (BoED), Mass Lesser Vigor (SpC), Recitation (SpC) and Righteous Wrath of the Faithful (SpC). The last four affect the whole party

Righteous Might is also eligible but not generally recommended as being Large sized all day can be inconvenient when dungeon-delving or otherwise being indoors.

If a spell is eligible to be chained it can be used in conjunction with a DMM Persisted spell, but if you want to pay for it using turn attempts rather than spell-slot increases, yes you'd need to take DMM twice.