Hello.
I passed over 40+ maps and got 63 wizard level, but do not yet got amplifier and spell panel. I already got different spells, but i do not see them.
http://gemcraft.wikia.com/wiki/List_of_Fields_in_Gemcraft_Chapter_2 has which tome gives what. I.e. amps are J4.
If you have the spell skills but can't use the spells, that'd be a bug. You should always have use of them after opening the right tome chamber except on vision fields.