[RPG] Can a Magus use Spellstrike and Spell Combat with spells prepared with other class slots

Your GM is correct. Spellstrike doesn't give you a free cast, what it allows you to do is turn your melee touch attack from casting a spell into a normal attack, allowing you to deal your weapon damage in addition to the spell.

At 2nd level, whenever a magus casts a spell with a range of “touch” from the magus spell list, he can deliver the spell through any weapon he is wielding as part of a melee attack. Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon (at his highest base attack bonus) as part of casting this spell.

Spellstrike Description on d20pfsrd.

So assuming I've got all my rules straight (someone please double check me on this) you would get a total of 5 melee attacks (4, 4, -1, 4, 4) plus one spell touch affect if at least one of those melee attacks hit. You use spell combat to cast a melee touch attack spell, which spellstrike turns into melee attack at highest BAB. You get your normal attacks, and your attacks from Speed and Sudden Attack. Since missing doesn't cost you your touch attack charge, you can keep trying to deliver your spell with each attack.

As Louis Huppenbauer pointed out, both using the Arcane Pool and Sudden Attack are swift actions, so making 5 melee attacks relies upon you having applied Speed in a previous round (it has a duration of 1 minute).

Spellstrike(Su) States:

At 2nd level, whenever a magus casts a spell with a range of “touch” from the magus spell list, he can deliver the spell through any weapon he is wielding as part of a melee attack. Instead of the free melee touch attack normally allowed to deliver the spell, a magus can make one free melee attack with his weapon (at his highest base attack bonus) as part of casting this spell.

If you missed while you had a charge of Shocking Grasp and that spell wasn't discharged, on the following round you can use an action to attack to discharge the spell and another action to cast another spell, which gives you a bonus attack. There's also a Caveat with Full Round Magus actions that I believe would be of interest to you as well:

From Spell Combat(Ex):

As a full-round action, he can make all of his attacks with his melee weapon at a –2 penalty and can also cast any spell from the magus spell list with a casting time of 1 standard action (any attack roll made as part of this spell also takes this penalty).

This meaning that at higher levels you would get multiple attacks as well as the bonus attack you get from Spellstrike after casting a spell as well.