For a small family company this is much simpler than the formation paperwork makes it look, so don’t overthink it.
Share capital is the nominal value of the shares you’ve issued. Issue 100 shares with a nominal value of £1 each and your share capital is £100. The nominal value is essentially arbitrary — £1 (or even 1p) per share is completely normal.
Share premium is anything paid above that nominal value. If someone pays £100 for a £1 share, £1 goes to share capital and £99 goes to the share premium account. That premium sits in a special non-distributable reserve: unlike profits, it can never be paid out as dividends. It’s mainly a creditor-protection device for when a company raises serious money above par.
So why did your friend split it £100 / £10,000? Almost certainly because an adviser wanted to put a sensible ‘price’ on the shares while keeping the nominal capital tiny — and once money is in the share premium account it’s locked in as part of the company’s permanent capital, which can reassure lenders. But for a family company it achieves very little you couldn’t get more simply.
And yes — you can absolutely just issue 100 £1 shares at par. £100 of share capital, fully paid, no premium account, no extra accounting. If you need to put more money into the company later, a director’s loan is far more flexible (and repayable) than share capital, which you generally can’t just take back.
To your last question: money sitting in the share premium account is usable in the business — it’s company cash like any other — it just can’t be distributed to shareholders as dividends.
On the paperwork: the statement of capital goes on your incorporation documents and each confirmation statement, any new allotment of shares must be filed at Companies House on form SH01 within a month, and you must keep statutory registers (members, persons with significant control) up to date. One tip: consider alphabet shares (A, B, C) at incorporation if family members might want different dividend rights later — much easier to set up now than to reorganise afterwards.