Thanks for the question, @ReportsSingular.
For both of the first two campaigns you provided—7ngs8 and 42l3d—the API stats match what’s shown on ads.twitter.com. We’re not seeing the 3,814 installs for the first campaign.
In terms of the billing issue, we’re seeing spend on 2017-04-08, as you mentioned, and then again on 2017-04-12. However, spend is slightly higher for the latter.
In general, recall that advertisers are billed when there is a qualifying event, such as an app click or install, if that event happens within a specific attribution window.
