I found this on Austrian's web site:
In addition to your carry-on baggage you may take one personal item with a maximum size of 40 x 30 x 10 cm into the passenger cabin, e.g. one lady's handbag or one laptop bag or one shoulder-strapped bag.
I've never seen an airline weigh the personal item, BUT I've never flown on Austrian.
I'm surprised at that 8kg limitation for an international flight (IAD-VIE). I did see it on Austrian's web site though. However, I also found this:
According to US-DOT (United States Department of Transportation) and CTA (Canadian Transportation Agency) regulations, it is the first carrier stated on your ticket who defines the baggage rules applicable to the entire journey.
The above suggests United's rules would govern if United is the carrier from LAX to IAD. But then maybe your ticket is a code-share and Austrian is the carrier for that leg also. I'm getting in over my head here. I hope you find an expert, or simply manage to stay within the most restrictive rules.
Regarding being late for a flight, look up "flat tire rule". It varies by airline, but essentially is an unwritten rule for mercy by the airline. You will take some comfort in its existence, but I wouldn't advise testing it casually.