Perhaps we should start back at the point you took employment. It seems to me as though you may have owned what the HMRC terms a personal service company. https://www.gov.uk/guidance/ir35-find-out-if-it-applies
These are typified by having one customer, and which is controlled by you or your associates, and where your work was controlled and overseen by your customer (i.e. as if you were an employee). In this circumstance the customer should have applied PAYE on your earnings. But, you didn't ask this.
The salary paid from a company to an employee can be whatever you want, subject to being 'reasonable' for the work actually undertaken. You did not have to pay a salary. You could have paid a dividend, or a company contribution to your pension. These options may be moot. If the only income you had during a year was 7,150 less your expenses then the split between salary and dividend and expenses won't make any difference because no tax is due on just that amount (but there is NI see below). More likely the amount was split between tax years, so you have to do the tax computations taking into account all your other earnings before concluding there is or isn't tax to pay.
You company had reporting obligations to HMRC https://www.gov.uk/paye-for-employers. The single payment you mentioned requires a payroll submission, and a P60. The company must also submit accounts to HMRC. The company must also report to Companies House quite a few details, in due course. These requirements if done by professionals usually mean that each company costs about 250 to 1000 p.a. to maintain compliance.
"...how can I prove what my expenses were, as they were all paid for on my personal account?" There is a difference between expenses undertaken as agent for the company, and those expenses you incurred in the course of your employment. The former can simply be reimbursed to you, and treated as an expense of the company. In other words the reported profit of the company is reduced by this expense and shows in company accounts. You probably want to figure out this part before declaring the rest as your employment income. The latter could be reimbursed by the company, but since that would trigger a benefit in kind declaration and another form, you might want instead to claim them as a deduction against your PAYE earnings, in your tax return.
"I managed to find receipts for fuel, etc, mounting to about £2000 to claim as expenses."
You can add to this home expenses and professional subscriptions, computers, communication costs. To qualify as deductions from your salary (and declared in your Tax Return), the expenses must have been incurred in the course of your employment (i.e. consultant to the customer) necessary to that employment, and you only claim the part that is 'wholly' an expense (i.e. apportion). But once again, this might be moot, because there may be no tax due anyway. As regards proof, actually a bank statement will do to prove a payment has been made, plus supporting documents if there's any doubt about what was paid for.
"Any other ways I can significantly reduce the amount of tax I pay, if I pay any at all?"
Well yes there are.. hundreds, but most of them are for very individual scenarios. Using the available personal allowances, UK resident married couples have been taking 60k annually with little tax. To work out the best combination, one would normally load a tax engine and start playing with the variables to find the combination that produces least overall tax.
You did not mention National Insurance. Depending upon how your income is split between tax years there is NI to pay. Usually that's a good thing because the UK State Pension is worth buying credits into for the minimal NI your company should pay for you. https://www.gov.uk/government/publications/cwg2-further-guide-to-paye-and-national-insurance-contributions/2019-to-2020-employer-further-guide-to-paye-and-national-insurance-contributions--3
HMRC are not going to show you how to put your accounts together, but they will take a pragmatic view of your best efforts if there is no tax at stake. However, whatever you put on the P60 is pretty much set in stone so think it all through before doing that bit.