Being wary and on your guard is good, but based on what you've written I think you're being a little paranoid (as are some other posters) and there are no red flags here in my opinion, especially after just 4 dates! That's not to say that you shouldn't be cautious, especially at this early stage. In particular, if he was married, he wouldn't have let you park outside his house or be holding hands with you in a place his son could see (irrespective of age).
1) His WhatsApp photo is blank (just the grey icon). This means nothing. I have a grey icon just because I haven't been bothered to include an image. Quite how this indicates that someone may be cheating I don't know!
He's not told me any really personal information about himself past the superficial stuff (like interests etc). I don't even know his surname.
As I wrote in a PP, not knowing his surname after 4 dates doesn't mean anything sinister. As for "really personal information", it's only been 4 dates... though if he guy was emotionally available, id expect him to be forthcoming soon. The lack of anything at this stage is your biggest concern imo, but that could just be caution on his part.
3. He only seems to be available just before work starting, just as he has finished work but before he's gone home, and late at night.
So he's messaging you at various points through the day... That's good! Various posters on here have said they feel even once daily messages are too intense early on! If he's got childcare responsibilities he's probably busy on the evenings - I know I am.
4. He doesn't call, only WhatsApp
I've been OLD since February... I'm a guy btw, and none of the women I've dated have ever called or suggested calling, not one, and I've had got to the 4 dates+ stage twice (with the current one still going well🙂) That's fine by me as I'm not really a caller myself. From my experience it seems most people aren't into calling these days.