There are two ways you can get the parent node.
Using JavaScript and using xPath.
1.) Using Javascript, you will have to use parentNode function to get the parent of an element.
Eg.
WebElement ele = driver.findElement(By.id("eleID"));
WebElement theParent = (WebElement) ((JavascriptExecutor) driver).executeScript("return arguments[0].parentNode;", ele );
2.) Using xPath, you can use ".." double dot to get the parent of the element.
Eg.
WebElement ele = driver.findElement(By.id("eleID"));
WebElement theParent = ele.findElement(By.xpath(".."));
To get the child element, you can simply identify element using xPath, cssSelector or tagName
Eg. Using tagName
WebElement eleTable = driver.findElement(By.id("TableID"));
WebElement theFirstRow = eleTable.findElements(By.tagName("tr")).get(0);