The first part is fine for DM's who feel that an outside source is different than a 'new spell'. Certainly, automatically knowing all spells on the spell list is as valid an interpretation. Personally I like the prayer method Zaister mentioned.
Divine spells SRD said:
Spells Gained at a New Level
Characters who can cast divine spells undertake a certain amount of study between adventures. Each time such a character receives a new level of divine spells, he or she learns new spells from that level automatically.
Independent Research
A divine spellcaster also can research a spell independently, much as an arcane spellcaster can. Only the creator of such a spell can prepare and cast it, unless he decides to share it with others.
arcane spells SRD said:
Independent Research
A wizard also can research a spell independently, duplicating an existing spell or creating an entirely new one.
Hmm, can't find the time or cost to research spells in SRD.
frankthedm said:
The player then finds out if it is accepted by the DM.
Good luck finding a quote to back that up.