Is it possible for the issued share capital of a company to be higher than it's authorized share capital?

Answer 1

No. A company can only issue shares up to what it's authorised to issue. Beyond that, it has first to increase its authorised share capital, then it can issue more shares.

What is authorised capital?
The amount of share capital stated in the memorandum of association is the company's 'authorised' capital. An entity's charter prescribes the number of ordinary shares that an entity is authorised to issue (authorised capital).

What is issued capital?
Issued capital is the value of the shares issued to shareholders. This means the nominal value of the shares rather than their actual worth. The amount of issued capital cannot exceed the amount of the authorised capital.

Can a company alter its authorised share capital?
A company can increase its authorised share capital by passing an ordinary resolution (unless its articles of association require a special or extraordinary resolution). A copy of the resolution - and notice of the increase on Form 123 - must reach Companies House within 15 days of being passed. No fee is payable to Companies House.
A company can decrease its authorised share capital by passing an ordinary resolution to cancel shares which have not been taken or agreed to be taken by any person. Notice of the cancellation, on Form 122, must reach Companies House within one month. No fee is payable to Companies House.

Answer 2

Yes, it is also quite common.

The number of issued shares is always less than or equal to the number of authorized shares.

In some areas, a company will be taxed based on the value of it's authorized shares.