Hmm - I like the idea of waiting a week to regain a cast spell. But...
1) magic items would become even more powerful in comparison (1/day mage armor amulet, shoes of spider climb 2/day, etc) - allowing the owner to outshine the caster in question.
2) low level play is difficult in extreme - a 1st level specialist wizard has, with INT bonus, 3 spells/day currently. Make that 3/week - once the wizard casts while in the dungeon, he is toast (melee or rng combat only since no spells for the rest of the week - yikes!).
3) bad guys are not impinged - unless you arbitrarily set up x spells not available for y days (2 days for 3 spells, 1 day for 1 spell, and 7 days for 3 spells) - and so unload true nasty on the pcs who will have already used up resources.
4) bookwork (as above, 1 week from time each spell is cast.....)
So: too extreme, but I like the concept.
1 answer) 1/day items are 1/wk
2 answer) allow each hp/day normally healed to be converted to recovery of 1 spell lv faster. That is, unwounded 1st lv wizard sleeps, regains 1 day on all spells plus +1 day for 1 spell. A 5th lv wizard can add 5 days between his spells. Good rest helps the casters a lot this way.
3 answer) make sure to assign spells cast earlier in the week - just more book keeping. Also, easier for PC's to harass and kill high level casters. Minor attacks over 5 days depletes most of his spell resources, make real attack on day 6.
4 answer) there is no answer - inherent with suggested idea.
BB