To setup a company, the prospect shareholders need to have few constitutional documents such as Memorandum of Association and Articles of Association (among the many docs)
In the Memorandum of Association, the prospect shareholders need to decide the maximum amount of capital that the company can issue. This amount is called the Authorized capital. This is a notional number. When setting up a company you really don’t need the entire capital in one go. Hence the shareholders decide to have a portion or part of the authorized capital to be issued. This portion of the capital which the shareholders actually decide to issue is called the Issued capital.
Once the shareholders pay up their share of the capital to the company, it becomes the paid up capital. . This is the physical money that the company actually gets to start its operations.
Now, once the Paid up capital is completely used and if the shareholders need additional capital, then they can get additional capital as the Paid Up capital is still less that the authorized capital. However, the company can issue additional capital only upto the Authorized capital.
If for some reason, they need to exceed the Authorized capital, then the necessary amendment need to be done in the Memorandum of association and then only the company can raise further capital.
With regard to taxation, to the best of my knowledge, tax is paid only when you make income and not on the capital and hence in my view there will not be any tax paid. However, based on the size of the authorized capital, there could be fees and other charges which SEBI or other agencies may charge.
With regard to face value of a share which is being started, it really does not matter at what level you want the face value to be. It can be 5,10,100. The only advantage with a higher value is, once the company is well established and doing really well and if the market value of the shares shoots up, you can split the shares until the face value becomes 1.
Classic example is MRF - the market value of one share is 68,233 with a face value of 10. With such high face value retail investors might not invest in these company in the secondary market which might make the share illiquid. If the company wants, they can split the share from face value from 10 to 1 and thereby reduce the market value to 6,823.3, so that there would be greater participation from all sections of investors.
Disclaimer: Not claiming to be an expert, there could be errors, please do your own research.