Yes, you can (at least with a standard merchant account)
You might have to send separate invoices for the different parts of the payment
Just make sure you specify in the invoice that it is a part payment and that you use the same email address every time.

Hi, think about registering in a virtual office. You can use their mailing services and the address. Using an office address will make you look more proffesional so this is another benefit

I agree with Simply Business. Also, try contacting some companies working as contractors for real estate agencies or make partners with someone who has a company for installing.
Social media marketing or ebay do not seem like a suitable strategy for your business.
Maybe try advertising on a more local level (villages small town etc) and you will have better luck

It is sad when society forces you to sell your hard work for $3 ..everyone looking to get the good work cheap....good luck anyways!

Hi, it depends on what you want to advertise and what is your target market.
Websites like Facebook or even Google can be quite good for advertising (Facebook especially for younger audience) but if you are targeting a specific group of people try their annual/monthly community newsletters, newspapers, articles etc