Is it ethical to receive a reimbursement for purchasing something that helps you perform your job but was not ordered by your boss to purchase if you don't work exactly 8 hours everyday as a salaried employee?
So as I understand it you bought something that would help you with your job without first asking your company if that was OK.
You won't be paid for this automatically. You have to ask to be paid, usually by submitting an expense claim for it. Submitting the claim is asking for it. If they agree to pay it that means they are OK. If not then they aren't. In the latter case you would be out of pocket by whatever you paid.
However simply submitting an expense claim does look a bit like you are trying to sneak recompense past the company. A better approach would be to ask your boss if it's OK to make the claim. If he says yes then you will be fine. If he doesn't, then you've spent some amount of your own money and need to accept that.
If they agree to pay then it's perfectly ethical to accept.
And unrelatedly if you aren't doing the hours required then start doing so.
As an employee, your employer has to supply you with the tools you need. (I was told that hairdressers can be counter examples, buying for example very expensive scissors and if any other employee including the boss touches them there is hell to pay).
Normally you ask your manager for what is needed, and it gets supplied. If not and you can’t work without the equipment you either tell them you can’t work and that’s it. Or you tell them you can’t work without the equipment and you’re going to buy it. In that case the company needs to reimburse you. If you don’t get reimbursed then the tools you bought disappear and you can’t work. The company still needs to pay you for your time when you can’t work through their fault.