Okay okay, I get that the eldritch knight doesn't grant new spells per level if you're a wizard, only bonus spells per day and an increase to "effective level of spell casting". Does this mean that a wizard who goes EK at level 6 (who knows level 1/2/3/ spells) can gather levels in eldritch knight for a while and learn level 5/6/7 spells when he levels in wizard again? Or are you stuck at level 3 spells?
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Spells per Day: At the indicated levels, an eldritch knight gains new spells per day as if he had also gained a level in an arcane spellcasting class he belonged to before adding the prestige class. He does not, however, gain any other benefit a character of that class would have gained, except for additional spells per day, spells known (if he is a spontaneous spellcaster), and an increased effective level of spellcasting. If a character had more than one arcane spellcasting class before becoming an eldritch knight, he must decide to which class he adds the new level for purposes of determining spells per day.
You don't learn the 2 free spells every time you get a level, but that is all.
You sill increase your spellcaster level and get access to the new levels of spells.
To answer your first question, then yes, when taking wizard levels, you can take whatever spell level your are able to cast (and learn per other means).
When you get a new wizard level, he chooses to spells from any level that he is able to cast (and not necessarily his highest level.
Spells Gained at a New Level: Wizards perform a certain amount of spell research between adventures. Each time a character attains a new wizard level, he gains two spells of his choice to add to his spellbook. The two free spells must be of spell levels he can cast. If he has chosen to specialize in a school of magic, one of the two free spells must be from his specialty school.