Single word that is used for all home-related services

Given that list of examples, Handyman is the first word that came to mind. The 2011 edition of Random House Kernerman Webster's College Dictionary has the definition I'm most familiar with which involves small maintenance or repair jobs. The definition from the fifth edition of The American Heritage Dictionary of the English Language also calls it a person who does odd jobs* or various small tasks.

The basic idea is that you are appending the suffix -man, which can be found in Collins English Dictionary – Complete and Unabridged (1991-2003), to indicate that you're a person with the profession or role of being handy. Handy means being good at manipulation or rather, work with the hand but it is being used primarily in an acquired sense of being generally useful, as emphasized below:

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3. Ready to the hand; near; also, suited to the use of the hand; convenient; valuable for reference or use; as, my tools are handy; a handy volume.

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Webster's Revised Unabridged Dictionary, 1913

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The example phrase, "he's handy around the home" in Collins Spanish Dictionary - Complete and Unabridged, 8th Edition, which seems to be an E.S.L. study aid, is actually fairly common in this sense of the word. You might also say someone or something comes in handy when it is useful, especially if it is conveniently available, as can be found to The American Heritage Dictionary of Idioms by Christine Amme (1997-2003).

According to the Online Etymology Dictionary, this word handyman being used for a generally useful person was first recorded in 1843. According to the nGrams chart below, this seems to have only started to gain popularity near the beginning of the 20th century as demonstrated by Google nGrams. Handyman certainly is not in Webster's 1844 American Dictionary of the English Language.

Although you may often replace -man with person with varying degrees of success for gender neutrality, this is almost unheard of with handyman, as the same Googl nGrams chart demonstrates. (You may see a screenshot of the chart here here, if necessary.)

*Odd job isn't technically single word but it's a phrase with special signification that refers to the whole spectrum of nonspecialized and unrelated jobs, especially for domestic or menial work. I suppose this could include driver. The principle idea is that you don't have a usual line of work, so you do many odd jobs on the side to suport yourself instead. You could call somebody who performs odd-jobs an odd-jobber. Unfortunately, this option does not refer to the "skill'd trades" like electrician but I figured it's worth mention if you do not want a more gender neutral word because you may call a person who does odd-jobs an odd-jobber, according to the fifth edition of the American Heritage Dictionary of the English Language.

The 2011 edition of Random House Kernerman Webster's College Dictionary might also call an odd jobber, just a jobber but I would not recommend that as the cited dictionary also seems to use several other definitions as well, including a type of stock-broker, a middleman and as a disparaging word referring to a corrupt and bought out politician.

I would consider picking something else but thesaurus.com doesn't even list any synonyms for handyman, aside from jack-of-all-trades which is not even close to a single word and hence will not be discussed. I think handyman may even be the only commonly recognizable word that even can cover all of these bases, without being overly ambiguous.