Based upon all you have written there is little to suggest that a cover letter would be especially helpful. It wouldn't do any harm, but I don't see anything that requires an act of wordsmithery or persuasive writing. So it's really optional in this case with the main objective to avoid introducing anything that would throw the application out-of-whack.
If you took it to a solicitor, they would compose a fairly neutral cover letter which took up these points...
- List of attachments: (itemized list of each piece of supporting evidence)
- Premise of the visit: (to maintain family relationships with a brief summary of the mechanics like length, where you will stay, and
- Current lifestyle circumstances: (explanation that you are married with children, explanation of why a visit is appropriate at
this particular point in time (important));
- Current economic circumstances: (explanation you are employed as a [==title==] at [==company==] since [==date==] earning
[==salary==], employment contract attached);
- Immigration history: (explanation that you were refused a long time ago but do not have precise records of the event);
- Other history: (criminal history if any. travel history if any);
The first page of the letter is devoted to the list of attachments, and the second page is devoted to your text. Because everything is (apparently) straightforward, you would be ill-advised to ramble beyond these two pages. You do NOT have to tell them that they are invited to contact you if they have further questions. They will wonder why you think it's important to raise that point. If you think your application is incomplete or will raise questions: do not submit it!
The letter itself is addressed to the "Consular Officer" at the post with cognizance for your application. If you do not know their name, the salutation is "To the Entry Clearance Officer:"
The subject line of the letter is:
Subject: Bob Cratchit, DOB: DD/MM/YYYY, Chinese national, GWF 00000000
Since this is such a plain vanilla case I do not see the need to copy the region or the Foreign Office Desk and certainly no reason to cc anyone in Parliament.
If the VFS tries to tell you that your letter is not required and removes it from your bundle (because they do stuff like that), it would be appropriate to make immediate representations.
Summary: based on everything you provided, the usefulness of a cover letter is marginal, you may be overthinking this part of the application.
In the income & expenditure where one is asked to indicate if I have
income and savings,should I click Yes or No. And if Yes should state
the ending balance as at the time of my application.
The key word here is "other", you answered the main questions in the previous section. Answer the questions using the natural meaning of the words so if you have 'other' put 'yes'.