Effects of changing the frequency of a transformer
I'll assume that your question is meant to  apply to power transformers intended for single phase AC mains use. My answer also applies more generally to some extent.

Summary:


For small changes in frequency - say a 60 Hz transformer run on 50 Hz,
kVA up slightly,
magnetising current up by MORE than 60/50,
inductance down somewhat,
induced voltage about the same,
losses much higher.
Death threatens.
E&amp;OE


AC mains power transformers are usually designed to make best use of the active material used to construct them - mainly the windings and the magnetic core. 

Power transfer relies on magnetic flux and the more the better (usually) so the core material (usually a laminated steel specially suited to the purpose) is arranged to have as much flux produced in it by the AC current in the primary winding.

The measure of the magnetising force is ampere-turns (H) and this is translated into magnetic flux (B) by the formula B = u.H where u (mu if i had Greek easily to hand and brain) is effectively a conversion factor.  If u was constant we could keep on adding H (more amp-turns) and getting more am more and more  output from a given core. Alas, there is a limit and above a given H level for a given material and various other conditions  we startto get proportionately less B. This is known as saturation. In practical terms we get more magnetic flux with more current up to a certain limit and above this we get less and less and less and ... return as we add more amps.

As the extra amps create losses in the copper and in the core and extra heat which tend todo bad things.

SO transformer manufacturers usually run their cores on the knee of saturation - at the point where the diminishing returns set in- so that they can get as much output as possible from the transformer. This affects the answers to your questions severely.


  If frequency of a transformer is decreased 


The lower frequency will see a lower impedance, there will be more current you will push further onto the non linear   knee of the BH curve, the transformer will be less  efficient but will handled somewhat more maximum power.

If you eg operate a transformer properly designed to run on 60 Hz it will get hot and unhappy on 50Hz even on no load. Ask me how I know ;-).


  keeping voltage same then what will be the new KVA rating


Somewhat higher as somewhat more B for you exrta H BUT for say 20% more current you may get 5% more flux and 5% more kVA out but 20% more kVa in AND 45% more copper losses.


  magnetising current 


mc will go up as there is less B per u - effectively the impedance has dropped.


  and inductance


Less inductance. Death is beckoning.


  induced voltage


Voltage is proportional to turns ratios and primary and secondary are linked by same flux so more or less the same voltage out. Secondary effects may change this slightly.


  and loss of transformer ?


Potentially total loss of transformer :-).
 A 60Hz transformer on 50 Hz runs hot.
 Make that wider and it would die. 
 An eg 400 Hz aircraft supply power transformer of any appreciable power would die faster than you could run when connected. 



E&amp;OE
 This can be a bit complex.
 Some of the above may be somewhat wrong in any given case - but probably right enough in most.