It does look as if David died before 1841, and given children born 1826, 1828, 1830 and 1833 he probably died around 1833 or not very long after.
ScotlandsPeople has the Old Parish Registers, post-1855 BMD certificates and census images online. You buy credits and then access whichever records you need. Scottish OPRs can be very hit and miss depending on which parish, and tend not to give much detail anyway, but are still worth researching. But death/burial records were not at all well kept: ScotlandsPeople has a list of which parishes have extant burial registers.
If the family followed the traditional Scottish naming pattern, and your David called his eldest son David, it's likely your David's father was also called David. And if he called his second daughter Catherine, then his mother could have been Catherine. However, not everyone followed the pattern exactly so it isn't sufficient evidence of parentage. Unfortunately, you don't know where he was born - he was in Shotts at the time of his marriage but could well have been born elsewhere.
