So Im a little new to small scale hydraulics like presses and such. I have been working on heavy machinery for my whole life but thats a whole other ball game. 

Im looking to get 12 tons on 120v. According to the online calculators I have been using, a 10.6 gpm 2 stage pump that puts out 3000 psi in high pressure paired with a 3.5” bore cylinder rated for 3000 psi should get me 4.2”/second in low pressure and hit just over 12 ton in high pressure... does this sound right? Now, the pump I am looking at calls for 5hp. Does this mean 5hp from a gas engine? In which case a 3hp electric should do no?? Please let me know if any of this is even close!! Thanks!

HP is HP whatever the power source as far as I know. A 5 hp combustion engine motor would be the same as a 5hp electric motor. 
 

5hp electric motor would be rated at around 3.75kW if that is what you were thinking of.  KW rating is around 3/4 of the hp rating number for number.   

1kW = 1.341hp

1hp = 0.7457kW

FWIW my 30 tonne double acting press has a a two stage pump and is rated at 50mm(2”)/sec up and 75mm(3”) /sec down

It uses a 2.25kW (3hp) motor to achieve that.

It has a 150mm (6”) diameter piston

Alan

Where do you get the idea Hp is different depending on how it is created? its like saying that ice cream is chocolate unless its Thursday then we call it lemon ?

Be aware that 5hp electric motor can produce that 5 hp forever, a 5hp gas engine is rated as 5hp max HP, but a continuous of about than half that so many times people use larger gas motors to get that 50% rating where they need it

Small, large, whatever, Hydraulics is hydraulics.  You're looking for someone on the internet to do the basic math for you, might as well throw the Tarot. 

To determine how hard it'll push, multiply PSI x piston area in sq/in. To determine ram speed divide cylinder volume in GALLONS by GPM.

You will need to convert psi from the ram to tons and speed to seconds, of course.

This is all basic math, asking a collection of random people on the internet is going to get a number of random opinions the majority from folk who only THINK they know what they're saying makes sense but is usually way off. HP is the last thing to decide because the requirement is based on the other two numbers. 

Frosty The Lucky.

Can someone please tell me a good electric air pump to get to power my new 12 ton Dab press

I don't know what you mean by an electric air pump for a press.

I can't control the wind, all I can do is adjust my sails. ~ Semper Paratus

Most likely the press is air over hydraulic.  Typically these are much too slow for effective forging, but better than nothing correctly setup.  You select a compressor based on both the compressed air flowrate and pressure your press is rated at (the compressor gets rated at a certain flow at a specific pressure.  beware of the ones where those two quantities are separated).  The motor should be continuous duty.  I'm not a big fan of oil free compressors and prefer two stage units, but YMMV.  Also remember you get what you pay for.  I was lucky to get a good second hand compressor from an auto repair place.  It was their backup unit, and lightly used, but it aged out.