bpaolo awesome questions to ask! It's important to know these things as you take responsibilities once you sell these products.
First of all many of the suppliers are traders and manufacturers. For Oberlo Supply we vet and visit the facilities so look for suppliers who are actually manufacturing the products themselves. This helps the Supply team source the lowest prices possible.
If you use Aliexpress you may find suppliers who say they are the manufacturer but actually aren't. There's not much you can do as you can't really validate it. You can always ask them but be wary as sometimes they send pictures from any manufacturer and say it's theirs.
In terms of compliance and safety that is something you have more control over. The are regulations the manufacturers have to follow so you can always request this information. In Aliexpress simply send them a message. For Oberlo Supply you can press the mail icon beside the supplier's name to ask.
For example, I was selling a steel flashlight and wanted to know what grade of steel it was. I messaged them through the app, the Supply Team escalated it to them and they scanned the certification in for me as a PDF! It was awesome!