Correct?

a. It is ages since I wrote you.
b. It ages since I wrote you.
Which one is correct?
2.
a. I know of none who deserves the prize more than you.
b. I know none who deserves the prize more than you.
Which one is correct?
3.
a. I was educated at St. Xaviers’ school.
a. I studied at St. Xaviers’ school.
Which one is correct?

a. Correct in AmE (BrE would be “wrote to you”).
b. Incorrect.

Both possible.

Both possible except that “St. Xaviers’” should be “St. Xavier’s”.

Isn’t there a difference between ‘‘It’s ages since I wrote to you’’ and ‘‘It’s been ages since I wrote to you’’?

Dozy/T_H_L,
“It is ages since I wrote to you.”
In this sentence is ‘ages’ a noun or an adjective?
Please clarify.
I know ‘ages’ is either a verb or a noun.
In this sentence how ‘ages’ works as a noun? To me it looks like an adjective.

Hi T_H_Lawrwnce!

 According to the researcher Michael Swan ("Practical English Usage")
"[b]It's ages[/b] since I wrote to you" --> more common in BrE  while

''It’s been ages since I wrote (*to) you" --> more common in AmE

*Note:
Americans say either [size=150]write to you[/size] or [size=150]write you[/size]
(that's with or without "to")
 Hi T_H_Lawrence!

According to the researcher Michael Swan (“Practical English Usage”)
“It’s ages since I wrote to you” → more common in BrE while
''It’s been ages since I wrote (*to) you" → more common in AmE

*Note:
Americans say either write to you or write you
(that’s with or without “to”)

I think a is correct

Not really.

It is a noun there.

‘Ages’ is a noun here, as Dozy has said. It is the plural of age, which means a very long period of time like the stone age, the atomic age etc.

The word ‘age’ can also be used as a verb and an adjective as you say.
To age is a natural phenomenon (Here it is a verb/infinitive).
I have an aged mother (here it is an adjective/participle)

I wonder how you have happened to say ‘ages’ looks like an adjective in ‘is ages’ or ‘has been ages’.

Now, ‘wrote to you’ and ‘wrote you’ are correct. Though it might be more AmE than BrE, I would prefer the latter (sans ‘to’). I have the following justification:

WRITE is a transitive verb (more specifically ditransitive such as GIVE and SHOW). A ditransitive verb takes two objects namely, direct (non personal) and indirect (personal). The practice is to place the personal object first without ‘to’. See the examples below and compare them:

I wrote him a letter (rather than ‘I wrote a letter to him’).
I gave him an apple (rather than ‘I gave an apple to him’).
I showed him the way (rather than ‘I showed the way to him’).

So, in my opinion, the personal object fits in and can be put there without ‘to’ whether the non personal object is explicit or implied.