I've offered some ideas/feedback ....I hope you are not offended by my offering specific examples of rewrites based on my suggestions.
I will not be offended or upset if you decide to ignore everything I say, for any reason(s). This is your cover letter, not mine!
I am an early 40's adult with excellent customer service and administration skills as well as skills in general IT and Internet such as email, word processing, Web searxching and Web page creation using HTML.
I suggest breaking this up, and shortening the bit about your computer skills.
I could be very wrong but I think it is assumed that most people can do web searches, use email, and use a word processor these days -- I'm pretty sure these things fall under basic computer skills or basic computer literacy.
I also suggest you move the bit about how fast you type to include it here, so all your computer-skills-things are grouped together.
For example:
"I am an early 40's adult with excellent customer service, administration, and general IT skills.
I can type accurately at speeds of up to 60 words per minute, and in addition to basic computer skills I am skilled at web page creation using HTML."
If you'd prefer to keep all of your examples of computer skills, I suggest you include the software and/or operating systems that you're familiar with, or just talk about how you are are familiar with multiple operating systems and a variety of software. For example:
"My IT skills include proficiency with email, word processing, and web searches on [operating system(s)] using [email clients, word processors]. I am skilled at web page creation using HTML and can type accurately at speeds of up to 60 words per minute"
I have an excellent telephone manner, and I am very open and approachable and eager to help customers at all times in any way I can. I can also type accurately at speeds of up to 60 words per minute.
This is good stuff, but awkwardly phrased (it's a run-on sentence, too many "ands" and a missing comma), I suggest breaking it up: Example:
"I have an excellent telephone manner and am very open and approachable. I am eager to help customers at all times, in any way I can."
(If you decide to leave it as a single sentence, I still strongly urge you to add the comma.)
And like I said before, I suggest you talk about your typing speed in the same section where you talk about your computer skills. (It seems like a non-sequitor if you put it in the paragraph where you go into detail about your customer service skills.)
My hobbies include video gaming, particularly on Xbox One and Android mobile phone, as well as training in Tae Kwon Do, a South Korean Martial Art, every Sunday evening and alternate Mondays and Fridays. My other hobbies include watching and playing Snooker and Pool, and attending regular Pub quiz nights on a weekly basis, I also enjoy singing on a Karaoke website and listening to retro music from the 60's, 70's and early to mid 80's.
I suggest you break up the sentences more so that each activity gets its own, or use semi-colons and make it like a list. I also suggest you take out the details about how often/when you engage in hobbies.
Example:
"My hobbies include: Video gaming, particularly on Xbox One and Android mobile phone; Training in Tae Kwon Do, a South Korean Martial Art; Watching and playing snooker and pool, and attending regular pub quiz nights. I also enjoy singing on a Karaoke website and listening to retro music from the 60's, 70's and early to mid 80's."
Also, I have to add myself to the people telling you that you shouldn't capitalize all names of things/nouns, only "proper names"/proper nouns. (The only place I have ever seen capitalization of all things/nouns is in archaic English from centuries ago.....today, it's grammatically incorrect.) If you are intent on capitalizing all names of things, your paragraph about hobbies should actually look like this:
"My Hobbies include video gaming, particularly on Xbox One and Android mobile Phone [or "Mobile Phone" -- depending on whether you consider "mobile" a part of the name of the thing, or a description of the thing], as well as training in Tae Kwon Do, a South Korean Martial Art, every Sunday Evening and alternate Mondays and Fridays. My other Hobbies include watching and playing Snooker and Pool, and attending regular Pub Quiz Nights on a weekly basis, I also enjoy singing on a Karaoke Website and listening to retro Music [or "Retro Music"] from the 60's, 70's and early to mid 80's."
.....because hobbies, phones, evenings, quizzes, nights, websites, and music are all names of things.
For place names,.....a house/home is a place, a street is a place, a yard is a place, a club is a place, a pub is a place, but you don't capitalize them. It has to be a name that belongs to a specific, individual place.
If you could consider me for your positions, I would be very grateful, however due to personal circumstances I am only available to work part time hours of up to 15 hours per week, please don't let that put you off giving me a chance to prove that I could be a real asset to your company.
It sounds like you are apologizing for the hours you can work, and it sounds like you expect the employer not to value you....these things could put employers off. It's best to seem confident, even if you aren't confident at all.
I recommend you just state that you are very grateful for the employer's consideration. No "if", just speak as if you assume they are considering you -- technically they are, or they wouldn't even bother reading your cover letter all the way through.....reading your cover letter and CV are the first parts of being considered for a job.
I also recommend you say the stuff about 15 hours per week and you can be a real asset to the company before you thank them.
I'm guessing you are sending these out, or posting this on a website, so that it's not specific to any particular job?
Example:
"I am available to work part time hours of up to 15 hours per week in any position you feel I'd be suitable for, and am very grateful for your consideration."