With starting spells, I interpret as these are the spells you learned during your "formal schooling" in magic. i.e. With a teacher helping you and plenty of time to get it just right. These are "gimme" spells. I personally don't use the learning rolls, but I wouldn't make a player roll for them, even the starting 2nd level spell. The PC knows them, even if he needs to advance a level before he is capable of channeling the more powerful magics of a 2nd level spell.
The way I run spells, a magic-user can find spells (e.g. scrolls or spell books) while adventuring and try to "learn" those by copying them into his own spellbook. The roll would be for properly copying the formulae and incantations so it would be memorizable later (spells per day). An MU can also learn spells when they level, the idea there is they visit the mage's guild library or meditate or research or experiment or whatever, trying to discover the proper components for whatever spell they are trying to gain. Some GMs only let MUs learn spells they've found (see above), some make them roll to see what they figured out when they level up, some let the player pick, depending on the kind of campaign they are running.
Min and Max spells? Well, I think quoting page 5 of the AEC is easiest here:
AEC5 wrote:Minimum Spells per Level: This number reflects the minimum number of spells any character with the equivalent INT should be able to learn per spell level. Normally, once a character has rolled and failed to learn a spell that character may never learn the spell. However, if a character has rolled to learn all spells in the spell listings (or rolled for all spells for that level that are available in the campaign) the character may roll again to try to learn a spell that was previously failed. The player may choose which spell to roll for again, but that spell may be rolled for again only once unless all other spells in that spell level have been rolled for again. Then if the minimum is still not met, the player may choose again and roll again and this process continues until the minimum number of spells is acquired.
Maximum Spells per Level: This number reflects the maximum number of spells any character with the equivalent INT should be able to learn per spell level. A character may have this maximum number available for memorization, and it should be noted that once the maximum number of spells are learned no other spells may be rolled for. This is true even if not all of the spells in the spell level have been rolled for.
Feel free to tweak to taste.