1) Can it be used with Spell Strike?
2) Can it be used in concert with Spell Combat?
If it is somehow added to a Magus' spell list, then yes, and yes. (Spell Blending, or Multiclass and Broad Study)
Calcific Touch: "Once per round, you may deliver a touch attack that inflicts 1d4 points of Dexterity damage and slows the target (as the spell) for 1 round."
Spell Combat allows you to cast that spell as your 'off-hand' attack.
Spellstrike lets you deliver that touch with your weapon, attacking full AC instead of touch AC, using the weapons critical threat range, and delivering both the spell and weapon damage on a hit.
The spell specifically restricts you to one attack per round, so if you cast the spell on round one, then make a full attack on round 2, you can only make one touch or spellstrike on round 2, the remainder of your attacks will not discharge the spell.
Same thing if you use Spell Combat and cast first. Cast the spell, get a free touch (which you can deliver with Spellstrike) then make full attack. The full attack will not discharge the spell (like it would with Chill Touch) because it is limited to once per round.
And, because it's bound to come up, "Target creature or creatures touched (up to one per level)" does not mean you can touch (Level) worth of creatures in one turn. That only works on willing targets (like Teleporting your party somewhere).
But the creatures you touch would get the Calcific Touch ability?
No, it's a touch spell, you cast it, then touch something to affect it.
Think of it as a personal 'buff' spell, you cast it, now when you touch an orc, bad stuff happens to it.
One thing to consider is that you only get an "extra" weapon+spell attack the FIRST round you cast Calcific Touch. Afterwards, while you're holding the charge, you either have to use a standard action touch attack OR add the leftover charges to your normal attacks. This can be tricky, because you can't use spell combat (or, for that matter, cast spells) in subsequent rounds without losing the leftover charges and wasting part of the spell.
I'm not saying that Calcific Touch is a bad idea (2d4 dex damage with a 15-20 crit range is nifty) but there are drawbacks.
1) It gives you a extra attack if you are using Spell Strike in concert with Spell Combat
While true, what really happens is you get a free touch attack as part of casting a touch spell. Any time you cast any touch spell, it grants you a free touch attack.
Spellstrike lets you make that touch attack with your weapon instead of a touch.
Spell Combat lets you cast that spell and make that touch, in place of your 'off-hand' attack, and also allowing you a normal full attack with your weapon.
2) Subsequent rounds of it will grant you a Calcific touch attack in the first attack that hits, say if you have three attacks and use Calcific Touch and discharge it.
Yes, your options are to use a standard action to make one touch attack, or you can use spellstrike once, your other attacks (if any) will not discharge Calcific Touch.
3) If you cast another spell you will lose the charges of Calcific Touch.
Yes.
I have a similar problem with my sorcerer/fighter, using a greatsword.
1)may I discharge Calcific Touch using one of my attack and continue attacking with the greatsword?(obviously not in casting round)
Only by making an unarmed strike, or attack with a natural weapon. Both vs normal AC. Making a touch attack is a standard action (or free as part of casting a touch spell)
"Iterative attacks are SOLELY the province of weapons (and of spells that specifically work like weapons)—touch attacks and natural weapons do not work this way." -James Jacobs (Creative Director)
3)Can I attack first with the greatsword(both hands on the sword), deliver the touch attack, and continue to attack with greatsword as a part of the full-attack?
No. Assuming you have more than one attack in a round, you could attack with the greatsword (2 hands) then bite or unarmed strike with a kick to deliver the spell. (The bite or kick is, once again, vs normal AC not touch) Once you've used your hand to wield a weapon, you can't let go and attack with it again.
I should make a Caveat here, some DMs will rule that as part of casting a touch spell, you have to choose what part of your body the spell is held in, and it's stuck there until you use it or cast a spell. They will generally not allow a magus to alternate between Spellstrike and touch attacks, saying that if the spell is "in" the sword, then you can't discharge it with a touch later, and vice versa.
If your DM rules this way, you may have a hard time with a held charge and using two hands on your weapon, unless the spell is defaulting to your foot (or bite or whatever).