2, What can happen if i donot use the 2 capacitors used across crystal. Do they shift frequency?

These two capacitors are extremely important! Together they form so called 'burden capacitance' and cause a well needed phase shift between oscillator output and input. A crystal oscillator without these two capacitors works like a car without wheels...
Omitting these two capacitors could indeed be the reason for your observed mismatch!

So, never omit them!!

1, How we can trim crystal oscillator for slight frequency adjustment. I know it can be done by small variable capacitor, but how i don't know. Can any one tell me about it.

This is normally explained in datasheet or application note. I'm generally not a fan of such a 'mechanical' adjusting, because quality of capacitance trimmer is not very good in many cases. Also, it's questionable whether you will ever find the optimum setting: If you need 24hours to get a mismatch of 15sec, how many days you would need to get this trimmed? And what about temperature dependency?
If you want to make this trimming, get the best and expensivest capacitance trimmer available. Use a type providing minimal temperature coefficient (unless differently recommended in datasheet!). TZBX4 (Murata) is a good choice, e.g. Use types with NPO material. It's a good idea to parallel a trimmer and a constant capacitance (also NP0).

There's one point that can cause heavy mismatch of time base, which is often overlocked: Some RTCs don't want to be accessed too often! These RTCs get the best accuracy when they are accessed as seldom as possible.
Also, in datasheet or application note sometimes there are methodes described, how they can be accessed without causing this frequency deviation.

Another cause for mismatch can be the interference from fast buses resulting in charge injection into oscilator section via parallel bus interface of RTC. Then, working with RTCs with serial interface can be helpful.

Kai