Search engines crawl the page and the site via internal links and index a page as they find it.
The most important place for targeted keywords is the off page SEO title that appears in blue in search results then the URL for the particular page which is in green below it. The meta description describing the page has no bearing on page rank.
R.E. the order of the words for page title i.e. service-town or town-service from an SEO perspective the keyword should come 1st before location,so for you Mike it would be Driveway Cleaning Hull. But no one seems to know why but it is an established fact amongst SEO pro's that page titles should be structured in that order for ranking purposes.
On page SEO - i.e. content - should have keywords in H1 tag - the headline at top of page and should only be 1 H1 tag otherwise it devalues it. Keywords should also appear in first paragraph and to a maximum of 2.5% of entire page content.
It is important to use synonyms and related search phrases rather than excessive keywords usage - or keyword stuffing as this can result in a penalty if detected by algorithms.
These are the main ways search engine decides on how to index your service and the more related terms that are used the more relevant the page is to a particular search term. A well optimised page can rank 1st for a search term that doesn't actually appear in its content if enough other factors and overall content make it appear to be the best and most relevant page.
There are over 200 ranking factors that can be assessed.
R.E. cleaners or cleaning,if you rank highly for one term that your page is optimised for you should find that you also rank well for the alternative even if you don't use it. Ideally both should appear throughout the content even if title,url etc concentrates on one.
As for search results,Google has placed more emphasis on 'local' and the results pages can differ depending on a person's location at the time of the search and proximity of local businesses to that person. Also your search history has a bearing on results and a company may rank slightly higher on results if the searcher has visited their site many times. So a search on a device you've never used before could produce a different results page to what your computer at home does.
Regarding search volumes they are available on Keyword Planner which is a tool to help with Adwords campaigns BUT they are NOT exact and only give approx monthly averages for a given area. usually 1-10 , 10-100, 100- 1000 etc. The only way to establish exact numbers is from running an actual ad which will show exact search terms used when your ad was displayed.
However,although search volumes are somewhat vague Keyword Planner does give the most relevant search terms and most popular.
Hope this is of some use.